Prof. Dr. Daniel Hug
- Sprecher der kollegialen Institutsleitung
- Raum: 2.051
CS 20.30 - Tel.: +49 721 608-43708
- daniel hug ∂does-not-exist.kit edu
- Englerstr. 2
76128 Karlsruhe
Forschung
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
Kurzbiographie
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
Bücher
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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
Publikationen
2025
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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 -
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 -
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 -
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 -
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 -
Hug, D.; Mussnig, F.; Ulivelli, J.
Additive kinematic formulas for convex functions
2025. Canadian Journal of Mathematics, 1–23. doi:10.4153/S0008414X24000944
2024
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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 -
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 -
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
2023
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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 -
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
2022
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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 -
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 -
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 -
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 -
Hug, D.; Schneider, R.
Threshold Phenomena for Random Cones
2022. Discrete and Computational Geometry, 67, 564–594. doi:10.1007/s00454-021-00323-2
2021
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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 -
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 -
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 -
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
2020
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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 -
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 -
Hug, D.; Schneider, R.
POISSON HYPERPLANE PROCESSES AND APPROXIMATION OF CONVEX BODIES
2020. Mathematika, 66 (3), 713–732. doi:10.1112/mtk.12040
2019
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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 -
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 -
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 -
Hug, D.; Thäle, C.
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
2018
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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 -
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 -
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 -
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 -
Hug, D.; Kabluchko, Z.
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
2017
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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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
Hug, D.; Schneider, R.
Rotation covariant local tensor valuations on convex bodies
2017. Communications in contemporary mathematics, 19 (5), 1650061. doi:10.1142/S0219199716500619
2016
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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 -
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 -
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 -
Hug, D.; Last, G.; Schulte, M.
Second-order properties and central limit theorems for geometric functionals of Boolean models1
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 -
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
2015
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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 -
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 -
Hinderer, W.; Hug, D.; Weil, W.
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 -
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 -
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
2014
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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 -
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 -
Hug, D.; Schneider, R.
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 -
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 -
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
2013
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Hug, D.; Last, G.; Pawlas, Z.; Weil, W.
Estimation of the radius distribution in the Boolen model of discs
2013. Program and Abstracts on the International Conference Geometry and Physics of Spacial Random Systems. Freudenstadt, 9-13 September 2013, 114–115 -
Hörrmann, J.; Hug, D.; Klatt, M.; Mecke, K.
Minkowski tensor density formulas for Boolen models
2013. Program and Abstracts on the International Conference Geometry and Physics of Spacial Random Systems. Freudenstadt, 9-13 September 2013, 98–99 -
Hug, D.; Last, G.; Schulte, M.
Second order properties and central limit theorems for geometric functionals of Boolean models
2013. Program and Abstracts on the International Conference Geometry and Physics of Spacial Random Systems. Freudenstadt, 9-13 September 2013, 73–74 -
Hug, D.; Türk, I.; Weil, W.
Flag measures for convex bodies
2013. Asymptotic geometric analsysis. Proceedings of the Fall 2010 Fields Institute Thematic Program, 145–187, Springer US. doi:10.1007/978-1-4614-6406-8_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 -
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 -
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 -
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 -
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 -
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
2011
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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 -
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 -
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 -
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
2010
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Hug, D.; Schneider, R.
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 -
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
2009
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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
2008
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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 -
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 -
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
2007
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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 -
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 -
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 -
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 -
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 -
Hug, D.
Random Mosaics
2007. Stochastic geometry : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 13 - 18, 2004. Ed.: W. Weil, 247–266, Springer-Verlag. doi:10.1007/978-3-540-38175-4_5
2006
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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
2005
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Hug, D.; Reitzner, M.
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 -
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 -
Hug, D.; Schneider, R.
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
2004
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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 -
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 -
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 -
Hug, D.; Munsonius, G. O.; Reitzner, M.
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 -
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
2003
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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
2002
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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 -
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 -
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 -
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 -
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 -
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
2001
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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 -
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
2000
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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 -
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 -
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 -
Hug, D.
Contact distributions of Boolean models
2000. Rendiconti del Circolo Matematico di Palermo Series 2. Supplemento, 65 (I), 137–181
1999
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Hug, D.
Absolute continuity for curvature measures of convex sets II
1999. Mathematische Zeitschrift, 232 (3), 437–485. doi:10.1007/PL00004765
1998
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Hug, D.
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
1996
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Hug, D.
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
1995
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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 -
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