Prof. Dr. Daniel Hug
- Speaker of the collegial institute management
- Room: 2.051
CS 20.30 - Phone: +49 721 608-43708
- daniel hug ∂does-not-exist.kit edu
- stoch.math.kit.edu/hug.php
- Englerstr. 2
76128 Karlsruhe
Research
Research interests
- Probability
- Geometry
- (Convex) geometric analysis
- Stochastic geometry and spatial stochastics
- Educational mathematics
DFG Priority Program: Random Geometric Systems (PP2265)
Geometry and Physics of Spatial Random Systems
Homepage of the former DFG research unit
Short biography
Preprints
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Bühler, T.; Hug, D.; Thaele, C.
Intersection density and visibility for Boolean models in hyperbolic space
2025. arxiv. doi:10.48550/arXiv.2501.13447 -
Hug, D.; Klatt, M. A.; Pabst, D.
Minkowski tensors for voxelized data: robust, asymptotically unbiased estimators
2025. arxiv. doi:10.48550/arXiv.2502.00092 -
Hug, D.; Last, G.; Schulte, M.
Boolean models in hyperbolic space
2024. arxiv. doi:10.48550/arXiv.2408.03890 -
Hug, D.; Mussnig, F.; Ulivelli, J.
Kubota-type formulas and supports of mixed measures
2024. arxiv. doi:10.48550/arXiv.2401.16371 -
Hug, D.; Schneider, R.
Vectorial analogues of Cauchy’s surface area formula
2023. doi:10.48550/arXiv.2307.12257 -
Betken, C.; Hug, D.; Thäle, C.
Intersections of Poisson -flats in constant curvature spaces
2023. doi:10.48550/arXiv.2302.09524
Books
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Hug, D.; Schneider, R.
Poisson Hyperplane Tessellations
2024. Springer Nature Switzerland. doi:10.1007/978-3-031-54104-9 -
Hug, D.; Weil, W.
Lectures on Convex Geometry
2020. Springer International Publishing. doi:10.1007/978-3-030-50180-8
Publications
Hug, D.; Reichenbacher, A.
Geometric inequalities, stability results and Kendall’s problem in spherical space
2025. Mathematika, 71 (4), Art.-Nr.: e70049. doi:10.1112/mtk.70049
Geometric inequalities, stability results and Kendall’s problem in spherical space
2025. Mathematika, 71 (4), Art.-Nr.: e70049. doi:10.1112/mtk.70049
Böröczky, K. J.; Fodor, F.; Hug, D.
Strengthened inequalities for the mean width and the -norm of origin symmetric convex bodies
2025. Mathematische Annalen, 393 (1), 271–316. doi:10.1007/s00208-025-03228-0
Strengthened inequalities for the mean width and the
2025. Mathematische Annalen, 393 (1), 271–316. doi:10.1007/s00208-025-03228-0
Bühler, T.; Hug, D.
Intersections of Poisson k -flats in hyperbolic space: Completing the picture
2025. Stochastic Processes and their Applications, 185, Art.-Nr.: 104613. doi:10.1016/j.spa.2025.104613
Intersections of Poisson k -flats in hyperbolic space: Completing the picture
2025. Stochastic Processes and their Applications, 185, Art.-Nr.: 104613. doi:10.1016/j.spa.2025.104613
Artstein-Avidan, S.; Hug, D.; Werner, E. M.
Convex Geometry and its Applications
2025. Oberwolfach Reports, 21 (4), 3301–3376. doi:10.4171/OWR/2024/58
Convex Geometry and its Applications
2025. Oberwolfach Reports, 21 (4), 3301–3376. doi:10.4171/OWR/2024/58
Hug, D.; Reichert, P. A.
Extremizers of the Alexandrov–Fenchel inequality within a new class of convex bodies
2025. Advances in Geometry, 25 (1), 13 – 38. doi:10.1515/advgeom-2024-0030
Extremizers of the Alexandrov–Fenchel inequality within a new class of convex bodies
2025. Advances in Geometry, 25 (1), 13 – 38. doi:10.1515/advgeom-2024-0030
Hug, D.; Mussnig, F.; Ulivelli, J.
Additive kinematic formulas for convex functions
2025. Canadian Journal of Mathematics, 1–23. doi:10.4153/S0008414X24000944
Additive kinematic formulas for convex functions
2025. Canadian Journal of Mathematics, 1–23. doi:10.4153/S0008414X24000944
Hug, D.; Reichert, P. A.
The support of mixed area measures involving a new class of convex bodies
2024. Journal of Functional Analysis, 287 (11), 110622. doi:10.1016/j.jfa.2024.110622
The support of mixed area measures involving a new class of convex bodies
2024. Journal of Functional Analysis, 287 (11), 110622. doi:10.1016/j.jfa.2024.110622
Hug, D.; Schneider, R.
Vectorial analogues of Cauchy’s surface area formula
2024. Archiv der Mathematik, 122 (3), 343–352. doi:10.1007/s00013-023-01962-y
Vectorial analogues of Cauchy’s surface area formula
2024. Archiv der Mathematik, 122 (3), 343–352. doi:10.1007/s00013-023-01962-y
Bartha, F. A.; Bencs, F.; Böröczky, K. J.; Hug, D.
Extremizers and Stability of the Betke–Weil Inequality
2024. Michigan Mathematical Journal, 74 (1), 45 – 71. doi:10.1307/mmj/20216063
Extremizers and Stability of the Betke–Weil Inequality
2024. Michigan Mathematical Journal, 74 (1), 45 – 71. doi:10.1307/mmj/20216063
Betken, C.; Hug, D.; Thäle, C.
Intersections of Poisson -flats in constant curvature spaces
2023. Stochastic Processes and their Applications, 165, 96 – 129. doi:10.1016/j.spa.2023.08.001
Intersections of Poisson
2023. Stochastic Processes and their Applications, 165, 96 – 129. doi:10.1016/j.spa.2023.08.001
Colesanti, A.; Hug, D.
Geometric and Functional Inequalities
2023. Convex Geometry : Cetraro, Italy 2021. Ed.: A. Colesanti, 79–158, Springer Nature Switzerland. doi:10.1007/978-3-031-37883-6_3
Geometric and Functional Inequalities
2023. Convex Geometry : Cetraro, Italy 2021. Ed.: A. Colesanti, 79–158, Springer Nature Switzerland. doi:10.1007/978-3-031-37883-6_3
Hug, D.; Santilli, M.
Curvature measures and soap bubbles beyond convexity
2022. Advances in Mathematics, 411 (Part A), Art.-Nr.: 108802. doi:10.1016/j.aim.2022.108802
Curvature measures and soap bubbles beyond convexity
2022. Advances in Mathematics, 411 (Part A), Art.-Nr.: 108802. doi:10.1016/j.aim.2022.108802
Ernesti, F.; Schneider, M.; Winter, S.; Hug, D.; Last, G.; Böhlke, T.
Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor
2022. Mathematical Methods in the Applied Sciences, 46 (1), 961–985. doi:10.1002/mma.8560
Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor
2022. Mathematical Methods in the Applied Sciences, 46 (1), 961–985. doi:10.1002/mma.8560
Göll, T.; Hug, D.
On a game of chance in Marc Elsberg’s thriller “GREED”
2022. Mathematische Semesterberichte, 69 (1), 103–139. doi:10.1007/s00591-021-00315-6
On a game of chance in Marc Elsberg’s thriller “GREED”
2022. Mathematische Semesterberichte, 69 (1), 103–139. doi:10.1007/s00591-021-00315-6
Böröczky, K. J.; Hug, D.
Reverse Alexandrov-Fenchel inequalities for zonoids
2022. Communications in Contemporary Mathematics, 24 (8), Art.Nr. 2150084. doi:10.1142/S021919972150084X
Reverse Alexandrov-Fenchel inequalities for zonoids
2022. Communications in Contemporary Mathematics, 24 (8), Art.Nr. 2150084. doi:10.1142/S021919972150084X
Hug, D.; Schneider, R.
Threshold Phenomena for Random Cones
2022. Discrete and Computational Geometry, 67, 564–594. doi:10.1007/s00454-021-00323-2
Threshold Phenomena for Random Cones
2022. Discrete and Computational Geometry, 67, 564–594. doi:10.1007/s00454-021-00323-2
Hug, D.; Schneider, R.
Another Look at Threshold Phenomena for Random Cones
2021. Studia scientiarum mathematicarum Hungarica, 58 (4), 489–504. doi:10.1556/012.2021.01513
Another Look at Threshold Phenomena for Random Cones
2021. Studia scientiarum mathematicarum Hungarica, 58 (4), 489–504. doi:10.1556/012.2021.01513
Hug, D.; Schneider, R.
Correction To: Integral geometry of pairs of hyperplanes or lines
2021. Archiv der Mathematik, 117 (6), 711–712. doi:10.1007/s00013-021-01657-2
Correction To: Integral geometry of pairs of hyperplanes or lines
2021. Archiv der Mathematik, 117 (6), 711–712. doi:10.1007/s00013-021-01657-2
Herold, F.; Hug, D.; Thäle, C.
Does a central limit theorem hold for the k-skeleton of Poisson hyperplanes in hyperbolic space?
2021. Probability Theory and Related Fields, 179 (3-4), 889–968. doi:10.1007/s00440-021-01032-w
Does a central limit theorem hold for the k-skeleton of Poisson hyperplanes in hyperbolic space?
2021. Probability Theory and Related Fields, 179 (3-4), 889–968. doi:10.1007/s00440-021-01032-w
Böröczky, K. J.; Fodor, F.; Hug, D.
Strengthened inequalities for the mean width and the ℓ-norm
2021. Journal of the London Mathematical Society, 104 (1), 233–268. doi:10.1112/jlms.12429
Strengthened inequalities for the mean width and the ℓ-norm
2021. Journal of the London Mathematical Society, 104 (1), 233–268. doi:10.1112/jlms.12429
Hug, D.; Schneider, R.
Integral geometry of pairs of hyperplanes or lines
2020. Archiv der Mathematik, 115, 339–351. doi:10.1007/s00013-020-01465-0
Integral geometry of pairs of hyperplanes or lines
2020. Archiv der Mathematik, 115, 339–351. doi:10.1007/s00013-020-01465-0
Böröczky, K. J.; Hug, D.
A reverse Minkowski-type inequality
2020. Proceedings of the American Mathematical Society, 148 (11), 4907–4922. doi:10.1090/proc/15133
A reverse Minkowski-type inequality
2020. Proceedings of the American Mathematical Society, 148 (11), 4907–4922. doi:10.1090/proc/15133
Hug, D.; Schneider, R.
POISSON HYPERPLANE PROCESSES AND APPROXIMATION OF CONVEX BODIES
2020. Mathematika, 66 (3), 713–732. doi:10.1112/mtk.12040
POISSON HYPERPLANE PROCESSES AND APPROXIMATION OF CONVEX BODIES
2020. Mathematika, 66 (3), 713–732. doi:10.1112/mtk.12040
Böröczky, K. J.; Fodor, F.; Hug, D.
Strengthened volume inequalities for zonoids of even isotropic measures
2019. Transactions of the American Mathematical Society, 371 (1), 505–548. doi:10.1090/tran/7299
Strengthened volume inequalities for
2019. Transactions of the American Mathematical Society, 371 (1), 505–548. doi:10.1090/tran/7299
Gardner, R. J.; Hug, D.; Xing, S.; Ye, D.
General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem II
2019. Calculus of variations and partial differential equations, 59, Article: 15. doi:10.1007/s00526-019-1657-2
General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem II
2019. Calculus of variations and partial differential equations, 59, Article: 15. doi:10.1007/s00526-019-1657-2
Hug, D.; Weil, W.
Determination of Boolean models by densities of mixed volumes
2019. Advances in applied probability, 51 (1), 116–135. doi:10.1017/apr.2019.5
Determination of Boolean models by densities of mixed volumes
2019. Advances in applied probability, 51 (1), 116–135. doi:10.1017/apr.2019.5
Hug, D.; Thäle, C.
Splitting tessellations in spherical spaces
2019. Electronic journal of probability, 24, 1–60. doi:10.1214/19-EJP267
Splitting tessellations in spherical spaces
2019. Electronic journal of probability, 24, 1–60. doi:10.1214/19-EJP267
Gardner, R. J.; Hug, D.; Weil, W.; Xing, S.; Ye, D.
General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem I
2019. Calculus of variations and partial differential equations, 58 (1), Art. Nr.: 12. doi:10.1007/s00526-018-1449-0
General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem I
2019. Calculus of variations and partial differential equations, 58 (1), Art. Nr.: 12. doi:10.1007/s00526-018-1449-0
Hug, D.; Weis, J. A.
Kinematic formulae for tensorial curvature measures
2018. Annali di matematica pura ed applicata, 197 (5), 1349–1384. doi:10.1007/s10231-018-0728-x
Kinematic formulae for tensorial curvature measures
2018. Annali di matematica pura ed applicata, 197 (5), 1349–1384. doi:10.1007/s10231-018-0728-x
Hug, D.; Rataj, J.; Weil, W.
Flag representations of mixed volumes and mixed functionals of convex bodies
2018. Journal of mathematical analysis and applications, 460 (2), 745–776. doi:10.1016/j.jmaa.2017.12.039
Flag representations of mixed volumes and mixed functionals of convex bodies
2018. Journal of mathematical analysis and applications, 460 (2), 745–776. doi:10.1016/j.jmaa.2017.12.039
Bernig, A.; Hug, D.
Kinematic formulas for tensor valuations
2018. Journal für die reine und angewandte Mathematik, 736, 141–191. doi:10.1515/crelle-2015-0023
Kinematic formulas for tensor valuations
2018. Journal für die reine und angewandte Mathematik, 736, 141–191. doi:10.1515/crelle-2015-0023
Hug, D.; Weis, J. A.
Crofton Formulae for Tensorial Curvature Measures: The General Case
2018. Analytic Aspects of Convexity. Ed.: G. Bianchi, 39–60, Springer International Publishing. doi:10.1007/978-3-319-71834-7_3
Crofton Formulae for Tensorial Curvature Measures: The General Case
2018. Analytic Aspects of Convexity. Ed.: G. Bianchi, 39–60, Springer International Publishing. doi:10.1007/978-3-319-71834-7_3
Hug, D.; Kabluchko, Z.
An inclusion-exclusion identity normal cones of polyhedral sets
2018. Mathematika, 64 (1), 124–136. doi:10.1112/S0025579317000390
An inclusion-exclusion identity normal cones of polyhedral sets
2018. Mathematika, 64 (1), 124–136. doi:10.1112/S0025579317000390
Hug, D.; Rataj, J.
Mixed curvature measures of translative integral geometry
2018. Geometriae dedicata, 195, 101–120. doi:10.1007/s10711-017-0278-1
Mixed curvature measures of translative integral geometry
2018. Geometriae dedicata, 195, 101–120. doi:10.1007/s10711-017-0278-1
Goodey, P.; Hinderer, W.; Hug, D.; Rataj, J.; Weil, W.
A flag representation of projection functions
2017. Advances in geometry, 17 (3), 303–322. doi:10.1515/advgeom-2017-0022
A flag representation of projection functions
2017. Advances in geometry, 17 (3), 303–322. doi:10.1515/advgeom-2017-0022
Weil, W.; Goodey, P.; Hug, D.
Kinematic formulas for area measures
2017. Indiana University Mathematics Journal, 66 (3), 997–1018. doi:10.1512/iumj.2017.66.6047
Kinematic formulas for area measures
2017. Indiana University Mathematics Journal, 66 (3), 997–1018. doi:10.1512/iumj.2017.66.6047
Hug, D.; Schneider, R.
Tensor Valuations and Their Local Versions
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E.V. Jensen, 27–65, Springer International Publishing. doi:10.1007/978-3-319-51951-7_2
Tensor Valuations and Their Local Versions
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E.V. Jensen, 27–65, Springer International Publishing. doi:10.1007/978-3-319-51951-7_2
Hug, D.; Klatt, M. A.; Last, G.; Schulte, M.
Second Order Analysis of Geometric Functionals of Boolean Models
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. Vedel Jensen, 339–383, Springer International Publishing. doi:10.1007/978-3-319-51951-7_12
Second Order Analysis of Geometric Functionals of Boolean Models
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. Vedel Jensen, 339–383, Springer International Publishing. doi:10.1007/978-3-319-51951-7_12
Hug, D.; Schneider, R.
SO(n) covariant local tensor valuations on polytopes
2017. Michigan mathematical journal, 66 (3), 637–659. doi:10.1307/mmj/1501034510
SO(n) covariant local tensor valuations on polytopes
2017. Michigan mathematical journal, 66 (3), 637–659. doi:10.1307/mmj/1501034510
Böröczky, K. J.; Hug, D.
Isotropic measures and stronger forms of the reverse isoperimetric inequality
2017. Transactions of the American Mathematical Society, 369 (10), 6987–7019. doi:10.1090/tran/6857
Isotropic measures and stronger forms of the reverse isoperimetric inequality
2017. Transactions of the American Mathematical Society, 369 (10), 6987–7019. doi:10.1090/tran/6857
Bernig, A.; Hug, D.
Integral geometry and algebraic structures for tensor valuations
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. B. Vedel Jensen, 79–109, Springer. doi:10.1007/978-3-319-51951-7_4
Integral geometry and algebraic structures for tensor valuations
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. B. Vedel Jensen, 79–109, Springer. doi:10.1007/978-3-319-51951-7_4
Hug, D.; Weis, J. A.
Crofton Formulae for Tensor-Valued Curvature Measures
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. B. Vedel Jensen, 111–156, Springer. doi:10.1007/978-3-319-51951-7_5
Crofton Formulae for Tensor-Valued Curvature Measures
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. B. Vedel Jensen, 111–156, Springer. doi:10.1007/978-3-319-51951-7_5
Colesanti, A.; Hug, D.; Gómez, E. S.
Monotonicity and concavity of integral functionals involving area measures of convex bodies
2017. Communications in contemporary mathematics, 19 (2), Art. Nr.: 1650033. doi:10.1142/S0219199716500334
Monotonicity and concavity of integral functionals involving area measures of convex bodies
2017. Communications in contemporary mathematics, 19 (2), Art. Nr.: 1650033. doi:10.1142/S0219199716500334
Hug, D.; Kiderlen, M.; Svane, A. M.
Voronoi-Based Estimation of Minkowski Tensors from Finite Point Samples
2017. Discrete & computational geometry, 57, 545–570. doi:10.1007/s00454-016-9851-x
Voronoi-Based Estimation of Minkowski Tensors from Finite Point Samples
2017. Discrete & computational geometry, 57, 545–570. doi:10.1007/s00454-016-9851-x
Hug, D.; Schneider, R.
Rotation covariant local tensor valuations on convex bodies
2017. Communications in contemporary mathematics, 19 (5), 1650061. doi:10.1142/S0219199716500619
Rotation covariant local tensor valuations on convex bodies
2017. Communications in contemporary mathematics, 19 (5), 1650061. doi:10.1142/S0219199716500619
Hug, D.; Reitzner, M.
Introduction to Stochastic Geometry
2016. Stochastic Analysis for Poisson Point Processes : Malliavin Calculus, Wiener-Itô Chaos, Expansions and Stochastic Geometry. Ed.: G. Peccati, 145–184, Springer. doi:10.1007/978-3-319-05233-5_5
Introduction to Stochastic Geometry
2016. Stochastic Analysis for Poisson Point Processes : Malliavin Calculus, Wiener-Itô Chaos, Expansions and Stochastic Geometry. Ed.: G. Peccati, 145–184, Springer. doi:10.1007/978-3-319-05233-5_5
Fodor, F.; Hug, D.; Ziebarth, I.
The volume of random polytopes circumscribed around a convex body
2016. Mathematika, 62 (1), 283–306. doi:10.1112/S0025579315000170
The volume of random polytopes circumscribed around a convex body
2016. Mathematika, 62 (1), 283–306. doi:10.1112/S0025579315000170
Barany, I.; Hug, D.; Schneider, R.
Affine diameters of convex bodies
2016. Proceedings of the American Mathematical Society, 144 (2), 797–812. doi:10.1090/proc12746
Affine diameters of convex bodies
2016. Proceedings of the American Mathematical Society, 144 (2), 797–812. doi:10.1090/proc12746
Hug, D.; Last, G.; Schulte, M.
Second-order properties and central limit theorems for geometric functionals of Boolean models
2016. The annals of applied probability, 26 (1), 73–135. doi:10.1214/14-AAP1086
Second-order properties and central limit theorems for geometric functionals of Boolean models
2016. The annals of applied probability, 26 (1), 73–135. doi:10.1214/14-AAP1086
Hug, D.; Schneider, R.
Random Conical Tessellations
2016. Discrete & computational geometry, 56 (2), 395–426. doi:10.1007/s00454-016-9788-0
Random Conical Tessellations
2016. Discrete & computational geometry, 56 (2), 395–426. doi:10.1007/s00454-016-9788-0
Bárány, I.; Hug, D.; Reitzner, M.; Schneider, R.
Random points in halfspheres
2016. Random structures & algorithms, 50 (1), 3–22. doi:10.1002/rsa.20644
Random points in halfspheres
2016. Random structures & algorithms, 50 (1), 3–22. doi:10.1002/rsa.20644
Hörrmann, J.; Hug, D.; Reitzner, M.; Thäle, C.
Poisson polyhedra in high dimensions
2015. Advances in mathematics, 281, 1–39. doi:10.1016/j.aim.2015.03.025
Poisson polyhedra in high dimensions
2015. Advances in mathematics, 281, 1–39. doi:10.1016/j.aim.2015.03.025
Hug, D.; Schneider, R.
Hölder continuity for support measures of convex bodies
2015. Archiv der Mathematik, 104 (1), 83–92. doi:10.1007/s00013-014-0719-0
Hölder continuity for support measures of convex bodies
2015. Archiv der Mathematik, 104 (1), 83–92. doi:10.1007/s00013-014-0719-0
Hinderer, W.; Hug, D.; Weil, W.
Extensions of translation invariant valuations on polytopes
2015. Mathematika, 61 (1), 236–258. doi:10.1112/S0025579314000187
Extensions of translation invariant valuations on polytopes
2015. Mathematika, 61 (1), 236–258. doi:10.1112/S0025579314000187
Kousholt, A.; Kiderlen, M.; Hug, D.
Surface tensor estimation from linear sections
2015. Mathematische Nachrichten, 288 (14-15), 1647–1672. doi:10.1002/mana.201400147
Surface tensor estimation from linear sections
2015. Mathematische Nachrichten, 288 (14-15), 1647–1672. doi:10.1002/mana.201400147
Gardner, R. J.; Hug, D.; Weil, W.; Ye, D.
The dual Orlicz-Brunn-Minkowski theory
2015. Journal of mathematical analysis and applications, 430 (2), 810–829. doi:10.1016/j.jmaa.2015.05.016
The dual Orlicz-Brunn-Minkowski theory
2015. Journal of mathematical analysis and applications, 430 (2), 810–829. doi:10.1016/j.jmaa.2015.05.016
Hug, D.; Thäle, C.; Weil, W.
Intersection and proximity of processes of flats
2015. Journal of mathematical analysis and applications, 426 (1), 1–42. doi:10.1016/j.jmaa.2014.12.068
Intersection and proximity of processes of flats
2015. Journal of mathematical analysis and applications, 426 (1), 1–42. doi:10.1016/j.jmaa.2014.12.068
Hug, D.; Schneider, R.
Approximation Properties of Random Polytopes Associated with Poisson Hyperplane Processes
2014. Advances in Applied Probability, 46 (4), 919–936. doi:10.1239/aap/1418396237
Approximation Properties of Random Polytopes Associated with Poisson Hyperplane Processes
2014. Advances in Applied Probability, 46 (4), 919–936. doi:10.1239/aap/1418396237
Hug, D.; Last, G.; Pawlas, Z.; Weil, W.
Statistics for Poisson Models of Overlapping Spheres
2014. Advances in Applied Probability, 46 (4), 937–962. doi:10.1239/aap/1418396238
Statistics for Poisson Models of Overlapping Spheres
2014. Advances in Applied Probability, 46 (4), 937–962. doi:10.1239/aap/1418396238
Hug, D.; Schneider, R.
Local Tensor Valuations
2014. Geometric and Functional Analysis, 24 (5), 1516–1564. doi:10.1007/s00039-014-0289-0
Local Tensor Valuations
2014. Geometric and Functional Analysis, 24 (5), 1516–1564. doi:10.1007/s00039-014-0289-0
Hörrmann, J.; Hug, D.
On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations
2014. Advances in Applied Probability, 46 (3), 622–642. doi:10.1239/aap/1409319552
On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations
2014. Advances in Applied Probability, 46 (3), 622–642. doi:10.1239/aap/1409319552
Hörrmann, J.; Hug, D.; Klatt, M. A.; Mecke, K.
Minkowski tensor density formulas for Boolean models
2014. Advances in applied mathematics, 55, 48–85. doi:10.1016/j.aam.2014.01.001
Minkowski tensor density formulas for Boolean models
2014. Advances in applied mathematics, 55, 48–85. doi:10.1016/j.aam.2014.01.001
Colesanti, A.; Hug, D.; Saorin Gomez, E.
A characterization of some mixed volumes via the Brunn-Minkowski inequality
2014. The journal of geometric analysis, 24, 1064–1091. doi:10.1007/s12220-012-9364-7
A characterization of some mixed volumes via the Brunn-Minkowski inequality
2014. The journal of geometric analysis, 24, 1064–1091. doi:10.1007/s12220-012-9364-7
Hug, D.; Rataj, J.; Weil, W.
A product integral representation of mixed volumes of two convex bodies
2013. Advances in Geometry, 13 (4), 633–662. doi:10.1515/advgeom-2012-0044
A product integral representation of mixed volumes of two convex bodies
2013. Advances in Geometry, 13 (4), 633–662. doi:10.1515/advgeom-2012-0044
Gardner, R. J.; Hug, D.; Weil, W.
Operations between sets in geometry
2013. Journal of the European Mathematical Society, 15 (6), 2297–2352. doi:10.4171/JEMS/422
Operations between sets in geometry
2013. Journal of the European Mathematical Society, 15 (6), 2297–2352. doi:10.4171/JEMS/422
Gardner, R. J.; Hug, D.; Weil, W.
The Orlicz-Brunn-Minkowski theory: A general framework, additions, and inequalities
2013. Journal of differential geometry, 97 (3), 427–476
The Orlicz-Brunn-Minkowski theory: A general framework, additions, and inequalities
2013. Journal of differential geometry, 97 (3), 427–476
Böröczky, K. J.; Fodor, F.; Hug, D.
Intrinsic volumes of random polytopes with vertices on the boundary of a convex body
2013. Transactions of the American Mathematical Society, 365, 785–809. doi:10.1090/S0002-9947-2012-05648-0
Intrinsic volumes of random polytopes with vertices on the boundary of a convex body
2013. Transactions of the American Mathematical Society, 365, 785–809. doi:10.1090/S0002-9947-2012-05648-0
Schröder-Turk, G. E.; Mickel, W.; Kapfer, S. C.; Schaller, F. M.; Breidenbach, B.; Hug, D.; Mecke, K.
Minkowski tensors of anisotropic spatial structure
2013. New Journal of Physics, 15 (August), 083028/1–38. doi:10.1088/1367-2630/15/8/083028
Minkowski tensors of anisotropic spatial structure
2013. New Journal of Physics, 15 (August), 083028/1–38. doi:10.1088/1367-2630/15/8/083028
Hug, D.
Random Polytopes
2013. Stochastic Geometry, Spatial Statistics and Random Fields - Asymptotic Methods. Ed.: E. Spodarev, 205–238, Springer-Verlag. doi:10.1007/978-3-642-33305-7_7
Random Polytopes
2013. Stochastic Geometry, Spatial Statistics and Random Fields - Asymptotic Methods. Ed.: E. Spodarev, 205–238, Springer-Verlag. doi:10.1007/978-3-642-33305-7_7
Hug, D.; Schneider, R.
Reverse inequalities for zonoids and their application
2011. Advances in mathematics, 228 (5), 2634–2646. doi:10.1016/j.aim.2011.07.018
Reverse inequalities for zonoids and their application
2011. Advances in mathematics, 228 (5), 2634–2646. doi:10.1016/j.aim.2011.07.018
Schröder-Turk, G. E.; Mickel, W.; Kapfer, S. C.; Klatt, M. A.; Schaller, F. M.; Hoffmann, M. J. F.; Kleppmann, N.; Armstrong, P.; Inayat, A.; Hug, D.; Reichelsdorfer, M.; Peukert, W.; Schwieger, W.; Mecke, K.
Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures
2011. Advanced Materials, 23 (22-23), 2535–2553. doi:10.1002/adma.201100562
Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures
2011. Advanced Materials, 23 (22-23), 2535–2553. doi:10.1002/adma.201100562
Hug, D.; Schneider, R.
Faces of Poisson-Voronoi mosaics
2011. Probability Theory and Related Fields, 151 (1-2), 125–151. doi:10.1007/s00440-010-0294-7
Faces of Poisson-Voronoi mosaics
2011. Probability Theory and Related Fields, 151 (1-2), 125–151. doi:10.1007/s00440-010-0294-7
Hug, D.; Schneider, R.
Faces with given directions in anisotropic Poisson hyperplane mosaics
2011. Advances in applied probability, 43 (2), 308–321. doi:10.1239/aap/1308662480
Faces with given directions in anisotropic Poisson hyperplane mosaics
2011. Advances in applied probability, 43 (2), 308–321. doi:10.1239/aap/1308662480
Hug, D.; Schneider, R.
Large faces in Poisson hyperplane mosaics
2010. The annals of probability, 38 (3), 1320–1344. doi:10.1214/09-AOP510
Large faces in Poisson hyperplane mosaics
2010. The annals of probability, 38 (3), 1320–1344. doi:10.1214/09-AOP510
Böröczky, K. J.; Hug, D.
Stability of the reverse Blaschke–Santaló inequality for zonoids and applications
2010. Advances in applied mathematics, 44 (4), 309–328. doi:10.1016/j.aam.2009.09.002
Stability of the reverse Blaschke–Santaló inequality for zonoids and applications
2010. Advances in applied mathematics, 44 (4), 309–328. doi:10.1016/j.aam.2009.09.002
Böröczky, K. J.; Fodor, F.; Hug, D.
The mean width of random polytopes circumscribed around a convex body
2010. Journal of the London Mathematical Society, 81 (2), 499–523. doi:10.1112/jlms/jdp077
The mean width of random polytopes circumscribed around a convex body
2010. Journal of the London Mathematical Society, 81 (2), 499–523. doi:10.1112/jlms/jdp077
Hug, D.
Nakajima’s problem for general convex bodies
2009. Proceedings of the American Mathematical Society, 137 (1), 255–263. doi:10.1090/S0002-9939-08-09432-X
Nakajima’s problem for general convex bodies
2009. Proceedings of the American Mathematical Society, 137 (1), 255–263. doi:10.1090/S0002-9939-08-09432-X
Böröczky, K. J., Jr; Hoffmann, L. M.; Hug, D.
Expectation of intrinsic volumes of random polytopes
2008. Periodica mathematica Hungarica, 57 (2), 143–164. doi:10.1007/s10998-008-8143-4
Expectation of intrinsic volumes of random polytopes
2008. Periodica mathematica Hungarica, 57 (2), 143–164. doi:10.1007/s10998-008-8143-4
Hug, D.; Schneider, R.; Schuster, R.
Integral geometry of tensor valuations
2008. Advances in applied mathematics, 41 (4), 482–509. doi:10.1016/j.aam.2008.04.001
Integral geometry of tensor valuations
2008. Advances in applied mathematics, 41 (4), 482–509. doi:10.1016/j.aam.2008.04.001
Hug, D.; Schneider, R.; Schuster, R.
The space of isometry covariant tensor valuations
2008. St. Petersburg mathematical journal, 19 (1), 137–158. doi:10.1090/S1061-0022-07-00990-9
The space of isometry covariant tensor valuations
2008. St. Petersburg mathematical journal, 19 (1), 137–158. doi:10.1090/S1061-0022-07-00990-9
Howard, R.; Hug, D.
Nakajima’s Problem: Convex Bodies of Constant Width and Constant Brightness
2007. Mathematika, 54 (1-2), 15–24. doi:10.1112/S0025579300000164
Nakajima’s Problem: Convex Bodies of Constant Width and Constant Brightness
2007. Mathematika, 54 (1-2), 15–24. doi:10.1112/S0025579300000164
Hug, D.; Schneider, R.
A stability result for a volume ratio
2007. Israel Journal of Mathematics, 161 (1), 209–219. doi:10.1007/s11856-007-0079-6
A stability result for a volume ratio
2007. Israel Journal of Mathematics, 161 (1), 209–219. doi:10.1007/s11856-007-0079-6
Hug, D.; Schneider, R.
Typical Cells in Poisson Hyperplane Tessellations
2007. Discrete & Computational Geometry, 38 (2), 305–319. doi:10.1007/s00454-007-1340-9
Typical Cells in Poisson Hyperplane Tessellations
2007. Discrete & Computational Geometry, 38 (2), 305–319. doi:10.1007/s00454-007-1340-9
Howard, R.; Hug, D.
Smooth convex bodies with proportional projection functions
2007. Israel Journal of Mathematics, 159 (1), 317–341. doi:10.1007/s11856-007-0049-z
Smooth convex bodies with proportional projection functions
2007. Israel Journal of Mathematics, 159 (1), 317–341. doi:10.1007/s11856-007-0049-z
Hug, D.; Schneider, R.
Asymptotic Shapes of large Cells in Random Tessellations
2007. GAFA Geometric And Functional Analysis, 17 (1), 156–191. doi:10.1007/s00039-007-0592-0
Asymptotic Shapes of large Cells in Random Tessellations
2007. GAFA Geometric And Functional Analysis, 17 (1), 156–191. doi:10.1007/s00039-007-0592-0
Hug, D.; Last, G.; Weil, W.
Polynomial parallel volume, convexity and contact distributions of random sets
2006. Probability Theory and Related Fields, 135 (2), 169–200. doi:10.1007/s00440-005-0459-y
Polynomial parallel volume, convexity and contact distributions of random sets
2006. Probability Theory and Related Fields, 135 (2), 169–200. doi:10.1007/s00440-005-0459-y
Hug, D.; Reitzner, M.
Gaussian polytopes: variances and limit theorems
2005. Advances in Applied Probability, 37 (2), 297–320. doi:10.1239/aap/1118858627
Gaussian polytopes: variances and limit theorems
2005. Advances in Applied Probability, 37 (2), 297–320. doi:10.1239/aap/1118858627
Hug, D.; Lutwak, E.; Yang, D.; Zhang, G.
On the Lp Minkowski Problem for Polytopes
2005. Discrete & Computational Geometry, 33 (4), 699–715. doi:10.1007/s00454-004-1149-8
On the Lp Minkowski Problem for Polytopes
2005. Discrete & Computational Geometry, 33 (4), 699–715. doi:10.1007/s00454-004-1149-8
Colesanti, A.; Hug, D.
Hessian Measures of Convex Functions and Applications to Area Measures
2005. Journal of the London Mathematical Society, 71 (01), 221–235. doi:10.1112/S0024610704005915
Hessian Measures of Convex Functions and Applications to Area Measures
2005. Journal of the London Mathematical Society, 71 (01), 221–235. doi:10.1112/S0024610704005915
Hug, D.; Schneider, R.
Large typical cells in Poisson-Delaunay mosaics
2005. Revue roumaine de mathématiques pures et appliquées, 50 (5-6), 657–670
Large typical cells in Poisson-Delaunay mosaics
2005. Revue roumaine de mathématiques pures et appliquées, 50 (5-6), 657–670
Gates, J.; Hug, D.; Schneider, R.
Valuations on Convex Sets of Oriented Hyperplanes
2005. Discrete & Computational Geometry, 33 (1), 57–65. doi:10.1007/s00454-004-1126-2
Valuations on Convex Sets of Oriented Hyperplanes
2005. Discrete & Computational Geometry, 33 (1), 57–65. doi:10.1007/s00454-004-1126-2
Hug, D.; Reitzner, M.; Schneider, R.
Large Poisson-Voronoi cells and Crofton cells
2004. Advances in Applied Probability, 36 (3), 667–690. doi:10.1239/aap/1093962228
Large Poisson-Voronoi cells and Crofton cells
2004. Advances in Applied Probability, 36 (3), 667–690. doi:10.1239/aap/1093962228
Heveling, M.; Hug, D.; Last, G.
Does polynomial parallel volume imply convexity?
2004. Mathematische Annalen, 328 (3), 469–479. doi:10.1007/s00208-003-0497-7
Does polynomial parallel volume imply convexity?
2004. Mathematische Annalen, 328 (3), 469–479. doi:10.1007/s00208-003-0497-7
Hug, D.; Schneider, R.
Large Cells in Poisson - Delaunay Tessellations
2004. Discrete and Computational Geometry, 31 (4), 503–514. doi:10.1007/s00454-003-0818-3
Large Cells in Poisson - Delaunay Tessellations
2004. Discrete and Computational Geometry, 31 (4), 503–514. doi:10.1007/s00454-003-0818-3
Hug, D.; Munsonius, G. O.; Reitzner, M.
Asymptotic mean values of Gaussian polytopes
2004. Beiträge zur Algebra und Geometrie, 45 (2), 531–548
Asymptotic mean values of Gaussian polytopes
2004. Beiträge zur Algebra und Geometrie, 45 (2), 531–548
Hug, D.; Last, G.; Weil, W.
A local Steiner–type formula for general closed sets and applications
2004. Mathematische Zeitschrift, 246 (1-2), 237–272. doi:10.1007/s00209-003-0597-9
A local Steiner–type formula for general closed sets and applications
2004. Mathematische Zeitschrift, 246 (1-2), 237–272. doi:10.1007/s00209-003-0597-9
Hug, D.; Reitzner, M.; Schneider, R.
The limit shape of the zero cell in a stationary Poisson hyperplane tessellation
2004. The Annals of Probability, 32 (1B), 1140–1167. doi:10.1214/aop/1079021474
The limit shape of the zero cell in a stationary Poisson hyperplane tessellation
2004. The Annals of Probability, 32 (1B), 1140–1167. doi:10.1214/aop/1079021474
Hug, D.; Last, G.; Weil, W.
Distance measurements on processes of flats
2003. Advances in Applied Probability, 35 (1), 70–95. doi:10.1239/aap/1046366100
Distance measurements on processes of flats
2003. Advances in Applied Probability, 35 (1), 70–95. doi:10.1239/aap/1046366100
Hug, D.; Mani-Levitska, P.; Schätzle, R.
Almost Transversal Intersections of Convex Surfaces and Translative Integral Formulae
2002. Mathematische Nachrichten, 246-247 (1), 121–155. doi:10.1002/1522-2616(200212)246:1<121::AID-MANA121>3.0.CO;2-G
Almost Transversal Intersections of Convex Surfaces and Translative Integral Formulae
2002. Mathematische Nachrichten, 246-247 (1), 121–155. doi:10.1002/1522-2616(200212)246:1<121::AID-MANA121>3.0.CO;2-G
Hug, D.
Absolute Continuity for Curvature Measures of Convex Sets, III
2002. Advances in Mathematics, 169 (1), 92–117. doi:10.1006/aima.2001.2055
Absolute Continuity for Curvature Measures of Convex Sets, III
2002. Advances in Mathematics, 169 (1), 92–117. doi:10.1006/aima.2001.2055
Hug, D.; Last, G.; Weil, W.
Generalized contact distributions of inhomogeneous Boolean models
2002. Advances in Applied Probability, 34 (1), 21–47. doi:10.1239/aap/1019160948
Generalized contact distributions of inhomogeneous Boolean models
2002. Advances in Applied Probability, 34 (1), 21–47. doi:10.1239/aap/1019160948
Hug, D.; Last, G.; Weil, W.
A Survey on Contact Distributions
2002. Morphology of Condensed Matter : Physics and Geometry of Spatially Complex Systems. Ed.: K. Mecke, 317–357, Springer-Verlag. doi:10.1007/3-540-45782-8_14
A Survey on Contact Distributions
2002. Morphology of Condensed Matter : Physics and Geometry of Spatially Complex Systems. Ed.: K. Mecke, 317–357, Springer-Verlag. doi:10.1007/3-540-45782-8_14
Hug, D.; Schneider, R.
Kinematic and Crofton formulae of integral geometry: recent variants and extensions
2002. Homenatge al professor Lluís Santaló i Sors: 22 de novembre de 2002. Editor: C. Barceló i Vidal, Càtedra de Lluís Santaló d’Aplicacions de la Matemàtica, 51–80, Universitat de Girona
Kinematic and Crofton formulae of integral geometry: recent variants and extensions
2002. Homenatge al professor Lluís Santaló i Sors: 22 de novembre de 2002. Editor: C. Barceló i Vidal, Càtedra de Lluís Santaló d’Aplicacions de la Matemàtica, 51–80, Universitat de Girona
Hug, D.; Schneider, R.
Stability results involving surface area measures of convex bodies
2002. Rendiconti del Circolo Matematico di Palermo Series 2. Supplemento, 70 (2), 21–51
Stability results involving surface area measures of convex bodies
2002. Rendiconti del Circolo Matematico di Palermo Series 2. Supplemento, 70 (2), 21–51
Hug, D.; Schätzle, R.
Intersections and Translative Integral Formulas for Boundaries of Convex Bodies
2001. Mathematische Nachrichten, 226 (1), 99–128. doi:10.1002/1522-2616(200106)226:1<99::AID-MANA99>3.0.CO;2-S
Intersections and Translative Integral Formulas for Boundaries of Convex Bodies
2001. Mathematische Nachrichten, 226 (1), 99–128. doi:10.1002/1522-2616(200106)226:1<99::AID-MANA99>3.0.CO;2-S
Gao, F.; Hug, D.; Schneider, R.
Intrinsic volumes and polar sets in spherical space
2001. Mathematicae Notae. Boletin del Instituto de Matematica ``Beppo Levi’’, 41, 159–176
Intrinsic volumes and polar sets in spherical space
2001. Mathematicae Notae. Boletin del Instituto de Matematica ``Beppo Levi’’, 41, 159–176
Hug, D.; Last, G.
On support measures in Minkowski spaces and contact distributions in stochastic geometry
2000. The Annals of Probability, 28 (2), 796–850. doi:10.1214/aop/1019160261
On support measures in Minkowski spaces and contact distributions in stochastic geometry
2000. The Annals of Probability, 28 (2), 796–850. doi:10.1214/aop/1019160261
Colesanti, A.; Hug, D.
Steiner type formulae and weighted measures of singularities for semi-convex functions
2000. Transactions of the American Mathematical Society, 352 (7), 3239–3263. doi:10.1090/S0002-9947-00-02671-4
Steiner type formulae and weighted measures of singularities for semi-convex functions
2000. Transactions of the American Mathematical Society, 352 (7), 3239–3263. doi:10.1090/S0002-9947-00-02671-4
Colesanti, A.; Hug, D.
Hessian measures of semi-convex functions and applications to support measures of convex bodies
2000. manuscripta mathematica, 101 (2), 209–238. doi:10.1007/s002290050015
Hessian measures of semi-convex functions and applications to support measures of convex bodies
2000. manuscripta mathematica, 101 (2), 209–238. doi:10.1007/s002290050015
Hug, D.
Contact distributions of Boolean models
2000. Rendiconti del Circolo Matematico di Palermo Series 2. Supplemento, 65 (I), 137–181
Contact distributions of Boolean models
2000. Rendiconti del Circolo Matematico di Palermo Series 2. Supplemento, 65 (I), 137–181
Hug, D.
Absolute continuity for curvature measures of convex sets II
1999. Mathematische Zeitschrift, 232 (3), 437–485. doi:10.1007/PL00004765
Absolute continuity for curvature measures of convex sets II
1999. Mathematische Zeitschrift, 232 (3), 437–485. doi:10.1007/PL00004765
Hug, D.
Absolute Continuity for Curvature Measures of Convex Sets I
1998. Mathematische Nachrichten, 195 (1), 139–158. doi:10.1002/mana.19981950108
Absolute Continuity for Curvature Measures of Convex Sets I
1998. Mathematische Nachrichten, 195 (1), 139–158. doi:10.1002/mana.19981950108
Hug, D.
Generalized curvature measures and singularities of sets with positive reach
1998. Forum Mathematicum, 10 (6), 699–728. doi:10.1515/form.10.6.699
Generalized curvature measures and singularities of sets with positive reach
1998. Forum Mathematicum, 10 (6), 699–728. doi:10.1515/form.10.6.699
Hug, D.
Contributions to affine surface area
1996. Manuscripta Mathematica, 91 (1), 283–301. doi:10.1007/BF02567955
Contributions to affine surface area
1996. Manuscripta Mathematica, 91 (1), 283–301. doi:10.1007/BF02567955
Hug, D.
Curvature Relations and Affine Surface Area for a General Convex Body and its Polar
1996. Results in mathematics, 29 (3-4), 233–248. doi:10.1007/BF03322221
Curvature Relations and Affine Surface Area for a General Convex Body and its Polar
1996. Results in mathematics, 29 (3-4), 233–248. doi:10.1007/BF03322221
Dolzmann, G.; Hug, D.
Equality of two representations of extended affine surface area
1995. Archiv der Mathematik, 65 (4), 352–356. doi:10.1007/BF01195547
Equality of two representations of extended affine surface area
1995. Archiv der Mathematik, 65 (4), 352–356. doi:10.1007/BF01195547
Hug, D.
On the mean number of normals through a point in the interior of a convex body
1995. Geometriae Dedicata, 55 (3), 319–340. doi:10.1007/BF01266322
On the mean number of normals through a point in the interior of a convex body
1995. Geometriae Dedicata, 55 (3), 319–340. doi:10.1007/BF01266322