# Publications

The textbook Lectures on Convex Geometry has been published in 2020 as vol. 286 in the Springer series Graduate Texts in Mathematics.

2021

112. T. Göll, D. Hug. On a game of chance in Marc Elsberg’s thriller ‘GREED’. Math. Semesterberichte. (to appear) pdf Python Code

111. K.J. Böröczky, D. Hug. Reverse Alexandrov--Fenchel inequalities for zonoids. Communications in Contemporary Mathematics (to appear) pdf

110. F.A. Bartha, F. Bencs, K.J. Böröczky, D. Hug. Extremizers and stability of the Betke--Weil inequality. Michigan Math. J. (to appear) pdf

109. D. Hug, R. Schneider. Another look at threshold phenomena for random cones. Studia Scientiarum Mathematicarum Hungarica: Combinatorics, Geometry and Topology (to appear) published online: https://doi.org/10.1556/012.2021.01513 pdf

108. F. Herold, D. Hug and Ch. Thäle. Does a central limit theorem hold for the \$k\$-skeleton of Poisson hyperplanes in hyperbolic space? Probab. Theory and Relat. Fields 179(3) (2021), 889--968. PTRF.Springer arxiv.pdf

107. D. Hug, J.A. Weis. Integral geometric formulae for Minkowski tensors. pdf

106. D. Hug, A. Reichenbacher. Geometric inequalities, stability results and Kendall's problem in spherical space. pdf

105. F. Ernesti, M. Schneider, S. Winter, D. Hug, G. Last, T. Böhlke: Characterizing digital microstructures by the Minkowski-based quadratic normal tensor pdf

104. D. Hug, R. Schneider: Threshold phenomena for random cones. Discrete Comput. Geom. (to appear) published online: https://link.springer.com/content/pdf/10.1007/s00454-021-00323-2.pdf pdf

103. K. Böröczky, F. Fodor and D. Hug. Strengthened inequalities for the mean width and the $l$-norm. J. London Math. Soc. 0 (2021), 1--36. pdf JLMS.pdf

2020

102. D. Hug and R. Schneider. Integral geometry of pairs of hyperplanes or lines. Arch. Math. 115 (2020), 339-–351. pdf

101. K. Böröczky and D. Hug. A reverse Minkowski-type inequality. Proc. Amer. Math. Soc. 148 (2020), 4907–-4922. pdf

100. D. Hug and R. Schneider. Poisson hyperplane processes and approximation of convex bodies. Mathematika 66 (2020), 713-–732 doi:10.1112/mtk.12040. pdf

99. Richard J. Gardner, Daniel Hug, Sudan Xing, Deping Ye. General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem II. Calculus of Variations and PDE's 59 no. 1, Paper No. 15 (2020), 33 pp. pdf

2019

98. K. Böröczky, F. Fodor and D. Hug. Strengthened volume inequalities for $L_p$ zonoids of even isotropic measures. Trans. Amer. Math. Soc. 371 (2019), 505--548. (electronically published July 20, 2018) https://doi.org/10.1090/tran/7299 pdf

97. D. Hug and Ch. Thäle. Splitting tessellations in spherical spaces. Electron. J. Probab. 24 (2019), paper no. 24, 60 pp. ISSN:1083-6489 https://doi.org/10.1214/19-EJP267 pdf

96. R. J. Gardner, D. Hug, W. Weil, S. Xing, D. Ye. General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I. Calculus of Variations and PDE's 58:12 (2019) 35 pp. https://doi.org/10.1007/s00526-018-1449-0(to appear) pdf

95. D. Hug and W. Weil. Determination of Boolean models by mean values of mixed volumes. Adv. Appl. Probab. 51 (2019), 116--135 pdf doi:10.1017/apr.2019.5

2018

94. D. Hug and J.A. Weis. Kinematic formulae for tensorial curvature measures. Annali di Matematica Pura ed Applicata (1923 -) (4) 197, no. 5, (2018), 1349--1384. (First Online: 30 January 2018) DOI 10.1007/s10231-018-0728-x pdf

93. D. Hug, J. Rataj and W. Weil. Flag representations of mixed volumes and mixed functionals of convex bodies. J. Math. Anal. Appl. 460 (2018), 745--776. https://doi.org/10.1016/j.jmaa.2017.12.039 pdf

92. D. Hug and Z. Kabluchko. An inclusion-exclusion identity for normal cones of polyhedral sets. Mathematika 64 (2018), 124--136. pdf

91. A. Bernig and D. Hug. Kinematic formulas for tensor valuations. J. Reine Angew. Math. 736 (2018), 141–-191 SSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0023, online first July 2015 pdf

2017

90. D. Hug and J.A. Weis. Crofton formulae for tensorial curvature measures: the general case. In: Analytic aspects of convexity (Gabriele Bianchi, Andrea Colesanti, Paolo Gronchi (eds.), Springer INdAM Series, Springer, 2017+ pdf

89. A. Bernig and D. Hug. Integral geometry and algebraic structures for tensor valuations. In: Lecture Notes in Mathematics, vol. 2177, ‘Tensor Valuations and their Applications in Stochastic Geometry and Imaging’ (eds. M. Kiderlen, Eva B. Vedel Jensen). 79--109. DOI 10.1007/978-3-319-51951-7_4pdf

88. D. Hug and R. Schneider. Rotation covariant local tensor valuations on convex bodies. Communications in Contemporary Mathematics 19 1650061-1--31, (2017) World Scientific Publishing Company DOI:10.1142/S0219199716500619 pdf

87. D. Hug and J.A. Weis. Crofton formulae for tensor-valued curvature measures. In: Lecture Notes in Mathematics, vol. 2177, ‘Tensor Valuations and their Applications in Stochastic Geometry and Imaging’ (eds. M. Kiderlen, Eva B. Vedel Jensen). 111--156. DOI 10.1007/978-3-319-51951-7_5 pdf

86. D. Hug and J. Rataj. Mixed curvature measures of translative integral geometry. Geom. Dedicata 195 (2018), 101--120. First Online: 18 August 2017. DOI 10.1007/s10711-017-0278-1. pdf

85. D. Hug and R. Schneider. SO$\left(n\right)$ covariant local tensor valuations on polytopes. Michigan Math. J. 66 (2017), 637--659. pdf

84. A. Colesanti, D. Hug. and E. Saorin Gomez. Monotonicity and concavity of integral functionals involving area measures of convex bodies. Communications in Contemporary Mathematics 19 (2017) 1650033-1--26 pdf

83. D. Hug, M.A. Klatt, G. Last and M. Schulte. Second order analysis of geometric functionals of Boolean models. In: Lecture Notes in Mathematics, vol. 2177, ‘Tensor Valuations and their Applications in Stochastic Geometry and Imaging’ (eds. M. Kiderlen, Eva B. Vedel Jensen). 339--383. DOI 10.1007/978-3-319-51951-7_12 pdf

82. D. Hug, M. Kiderlen, A. M. Svane. Voronoi-based estimation of Minkowski tensors from finite point samples. Discrete Comput. Geom. 57 (2017), 545--570. pdf

81. D. Hug and R. Schneider. Tensor valuations and their local versions. In: Lecture Notes in Mathematics, vol. 2177, ‘Tensor Valuations and their Applications in Stochastic Geometry and Imaging’ (eds. M. Kiderlen, Eva B. Vedel Jensen). 27--65. DOI 10.1007/978-3-319-51951-7_2 pdf

80. P. Goodey, D. Hug and W. Weil. Kinematic formulas for area measures. Indiana Univ. Math. J. 66(3) (2017), 997--1018 pdf

79. I. Barany, D. Hug, M. Reitzner and R. Schneider. Random points in halfspheres. Random Structures Algorithms 50 (2017), 3--22. pdf

78. P. Goodey, W. Hinderer, D. Hug, J. Rataj and W. Weil. A flag representation of projection functions. Adv. Geom. 17(3) (2017), 303–-322. pdf

77. K. Böröczky and D. Hug. Isotropic measures and stronger forms of the reverse isoperimetric inequality. Trans. Amer. Math. Soc. 369(10) (2017), 6987--7019. http://dx.doi.org/10.1090/tran/6857 pdf

2016

76. D. Hug and R. Schneider. Random conical tessellations. Discrete Comput. Geom. 52 (2016), 395--426. pdf

75. F. Fodor, D. Hug and I. Ziebarth. The volume of random polytopes circumscribed around a convex body. Mathematika 62 (2016), 283-306. pdf

74. I. Barany, D. Hug and R. Schneider. Affine diameters of convex bodies. Proc. Amer. Math. Soc. 144 (2016), 797-812. DOI: http://dx.doi.org/10.1090/proc12746 Published electronically: May 28, 2015 pdf

73. D. Hug and M. Reitzner. Introduction to Stochastic Geometry. In ``Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Ito Chaos Expansions and Stochastic Geometry", edited by Giovanni Peccati and Matthias Reitzner, Bocconi & Springer Series, Vol. 7, 145-184 Springer, 2016. pdf

72. D. Hug, G. Last and M. Schulte. Second-order properties and central limit theorems for geometric functionals of Boolean models. Ann. Appl. Probab. 26 (2016), 73-135. pdf

2015

71. R.J. Gardner, D. Hug and W. Weil, D. Ye. The dual Orlicz-Brunn-Minkowski theory. J. Math. Anal. Appl. 430 (2015), 810--829. pdf

70. D. Hug, Ch. Thäle and W. Weil. Intersection and proximity of processes of flats. J. Math. Anal. Appl. 426 (2015), 1-42. pdf

69. A. Kousholt, M. Kiderlen and D. Hug. Surface tensor estimation from linear sections. Math. Nachr. 288 (2015), 1647-1672. Article first published online: 28 APR 2015 DOI: 10.1002/mana.201400147 pdf

68. J. Hörrmann, D. Hug, M. Reitzner and Ch. Thäle. Poisson polyhedra in high dimensions. Adv. Math. 281 (2015), 1-39. pdf

67. D. Hug and R. Schneider. Hölder continuity of support measures of convex bodies. Arch. Math. 104 (2015), 83-92. pdf

66. W. Hinderer, D. Hug and W. Weil. Extensions of translation invariant valuations on polytopes. Mathematika 61 (2015) 236-258. pdf

2014

65. D. Hug and R. Schneider. Local tensor valuations. Geom. Funct. Anal. 24 (2014), 1516-1564. pdf

64. D. Hug, G. Last, Z. Pawlas and W. Weil. Statistics for Poisson models of overlapping spheres. Adv. Appl. Probab. 46 (2014),937-962. pdf

63. J. Hörrmann, D. Hug, M. Klatt and K. Mecke. Minkowski tensor density formulas for Boolean models. Adv. Appl. Math. 55 (2014), 48-85. pdf

62. D. Hug and R. Schneider. Approximation properties of random polytopes associated with Poisson hyperplane processes. Adv. Appl. Probab. 46 (2014), 919-936. pdf

61. J. Hörrmann and D. Hug. On the volume of the zero cell of a class of isotropic Poisson hyperplane tessellations. Adv. Appl. Probab. 46 (2014), 622-642. pdf

60. R.J. Gardner, D. Hug and W. Weil. The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities. J. Differential Geom. 97 (2014), 427-476. pdf

2013

59. R.J. Gardner, D. Hug and W. Weil. Operations between sets in geometry. J. Europ. Math. Soc. 15 (2013), 2297–2352. pdf

58. D. Hug. Random polytopes. In: Stochastic Geometry, Spatial Statistics and Random Fields. Asymptotic Methods. Lecture Notes in Mathematics 2068 (ed. Evgeny Spodarev) (2013), 205-238. 61.pdf|pdf

57. D. Hug, I. Türk and W. Weil. Flag measures for convex bodies. Fields Institute Communications (eds. Monika Ludwig, Vitali D. Milman, Vladimir Pestov, Nicole Tomczak-Jaegermann) 68 (2013), 145-187. pdf

56. D. Hug, J. Rataj and W. Weil. A product integral representation of mixed volumes of two convex bodies. Adv. Geom. 13 (2013), 633-662. pdf

55. G.E. Schröder-Turk, W. Mickel, S.C. Kapfer, F.M. Schaller, B. Breidenbach, D. Hug and K. Mecke. Minkowski tensors of anisotropic spatial structure. New J. Phys. 15 (2013), 083028 pdf

54. K. Böröczky, F. Fodor and D. Hug. Intrinsic volumes of random polytopes with vertices on the boundary of a convex body. Trans. Amer. Math. Soc. 365 (2013), 785--809. pdf

2012

53. A. Colesanti, D. Hug. and E. Saorin Gomez. A characterization of some mixed volumes via the Brunn-Minkowski inequality. J. Geom. Analysis 24, Issue 2, (2014), 1064--1091 (appeared online 10 October 2012, DOI 10.1007/s12220-012-9364-7) pdf

2011

52. G.E. Schröder-Turk, W. Mickel, S.C. Kapfer, M.A. Klatt, F.M. Schaller, M.J.F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, K. Mecke. Minkowski Tensor shape analysis of cellular, granular and porous structures. Advanced Materials, Special Issue: Hierarchical Structures Towards Functionality. 23 (2011), 2535–2553. Wiley

51. D. Hug, R. Schneider. Reverse inequalities for zonoids and their application. Adv. Math. 228 (2011), 2634-2646. doi:10.1016/j.aim.2011.07.018

50. D. Hug, R. Schneider. Faces with given directions in anisotropic Poisson hyperplane tessellations. Adv. Appl. Probab. 43 (2011), 308-321. pdf

49. D. Hug, R. Schneider. Faces in Poisson-Voronoi mosaics. Probab. Theory and Relat. Fields. 151 (2011), 125-151. pdf Official journal site

2010

48. K. Böröczky, D. Hug. Stability of the reverse Blaschke-Santalo inequality for zonoids and applications. Adv. Appl. Math. 44 (2010), 309-328. pdf

47. D. Hug, R. Schneider. Large faces in Poisson hyperplane mosaics. Ann. Probab. 38 (2010), 1320-1344. pdf Official journal site

46. K. Böröczky, F. Fodor, D. Hug. The mean width of random polytopes circumscribed around a convex body. J. London Math. Soc. 81 (2010), 499–523. pdf

2009

45. D. Hug. Nakajima's problem for general convex bodies. Proc. Amer. Math. Soc. 137 (2009), 255-263. pdf

2008

44. K. Böröczky, L.M. Hoffmann, D. Hug. Expectation of intrinsic volumes of random polytopes. Periodica Mathematica Hungarica 57 (2008), 143-164. pdf

43. D. Hug, R. Schneider, R. Schuster. Integral geometry of tensor valuations. Adv. Appl. Math. 41 (2008), 482-509. pdf

42. D. Hug, R. Schneider, R. Schuster. The space of isometry covariant tensor valuations.
Algebra i Analiz and St. Petersburg Math. J. 19 (2008), 137-158. pdf

2007

41. R. Howard, D. Hug. Nakajima's problem: convex bodies of constant width and constant brightness. Mathematika 54 (2007), 15-24. pdf

40. R. Howard, D. Hug. Smooth convex bodies with proportional projection functions. Israel J. Math. 159 (2007), 317-341. pdf

39. D. Hug, R. Schneider. Typical cells in Poisson hyperplane tessellations. Discrete Comput. Geom. 38 (2007), 305-319. pdf

38.
D. Hug, R. Schneider. A stability result for a volume ratio. Israel J. Math. 161 (2007), 209-219. pdf

37. D. Hug, R. Schneider. Asymptotic shapes of large cells in random tessellations. Geom. Funct. Anal. 17 (2007), 156-191. pdf

36. D. Hug. Random mosaics. pp. 247--266. In: Baddeley, A.; Bárány, I.; Schneider, R.; Weil, W. Stochastic geometry. Edited by W. Weil. Lecture Notes in Mathematics, 1892. Springer-Verlag, Berlin, 2007. pdf

2006

35. D. Hug. Modellieren und Entscheiden bei Ungewissheit (Stochastik in Klasse 11), 30 Seiten + Anhang, Dokumentation einer Unterrichtseinheit im Rahmen der zweiten Staatsprüfung für die Laufbahn des höheren Schuldienstes an Gymnasien (18 monatiger Vorbereitungsdienst), Landeslehrerprüfungsamt, Regierungspräsidium Freiburg, Abteilung 7 und Staatliches Seminar für Didaktik und Lehrerbildung (Gymnasien) Freiburg, Freiburg, 05. Januar 2006. pdf

34.
D. Hug, G. Last, W. Weil. Polynomial parallel volume, convexity and contact distributions of random sets. Probab. Theory and Relat. Fields 135 (2006), 169-200. pdf

2005

33. D. Hug, R. Schneider. Large Typical Cells in Poisson-Delaunay Mosaics, Rev. Roumaine Math. Pures Appl. 50 (2005), 657-670. pdf

32. A. Colesanti and D. Hug. Hessian measures of convex functions and area measures. J. London Math. Soc. 71 (2005), 221-235. pdf

31. D. Hug, M. Reitzner. Gaussian polytopes: variances and limit theorems, Adv. Appl. Probab. 37 (2005), 297-320. pdf

30. D. Hug, E. Lutwak, Deane Yang, Gaoyong Zhang. On the ${L}_{p}$ Minkowski problem for polytopes. Discrete Comput. Geom. 33 (2005), 699-715. pdf

29. J. Gates, D. Hug, R. Schneider. Valuations on convex sets of oriented hyperplanes. Discrete Comput. Geom. 33 (2005), 57-65. pdf

2004

28. D. Hug, G.O. Munsonius, M. Reitzner. Asymptotic mean values of Gaussian polytopes. Contributions to Algebra and Geometry 45 (2004), 531-548. pdf

27. D. Hug, M. Reitzner, R. Schneider. Large Poisson-Voronoi cells and Crofton cells. Adv. Appl. Probab. 36 (2004), 667-690. pdf

26. D. Hug, R. Schneider. Large cells in Poisson-Delaunay tessellations. Discrete Comput. Geom. 31 (2004), 503-514.pdf

25. D. Hug, M. Reitzner, R. Schneider. The limit shape of the zero cell in a stationary Poisson hyperplane tessellation. Ann. Probab. 32 (2004), 1140-1167. pdf

24. M. Heveling, D. Hug, G. Last. Does polynomial parallel volume imply convexity? Math. Ann. 328 (2004), 469-479. pdf

23. D. Hug, G. Last, W. Weil. A local Steiner-type formula for general closed sets and applications. Math. Z. 246 (2004), 237-272. pdf

2003

22. D. Hug, G. Last, W. Weil. Distance measurements on processes of flats. Adv. Appl. Probab. 35 (2003), 70-95. pdf

21. F. Gao, D. Hug, R. Schneider. Intrinsic volumes and polar sets in spherical space. Math. Notae 41 (2001/02), 159-176 (2003). pdf

2002

20. D. Hug, R. Schneider. Kinematic and Crofton formulae of integral geometry: recent variants and extensions. (Survey) pp. 51-80. Homenatge al professor Lluís Santaló i. Sors: 22 de novembre de 2002 / C. Barceló i Vidal (ed.), Girona: Universitat de Girona. Càtedra Lluís Santaló d'Aplicacions de la Matemàtica, 2002. pdf

19. D. Hug, R. Schneider. Stability results involving surface area measures of convex bodies. Rend. Circ. Mat. Palermo (2) Suppl. No. 70, part II (2002), 21--51. pdf

18. D. Hug, G. Last, W. Weil. A survey on contact distributions. pp. 317-357. Statistical Physics and Spatial Statistics, Lecture Notes in Physics 600, Morphology of Condensed Matter, Physics and Geometry of Spatially Complex Systems, ed. by K. Mecke and D. Stoyan, Springer, Berlin, 2002. pdf

17. D. Hug, G. Last, W. Weil. Generalized contact distributions of inhomogeneous Boolean models. Adv. Appl. Probab. 34 (2002), 21-47. pdf

16. D. Hug, P. Mani-Levitska and R. Schätzle. Almost transversal intersections of convex surfaces and translative integral formulae. Math. Nachr. 246-247 (2002), 121-155. pdf

15. D. Hug. Absolute continuity for curvature measures of convex sets III. Adv. Math. 169 (2002), 92-117. pdf

2001

14. D. Hug and R. Schätzle. Intersections and translative integral formulas for boundaries of convex bodies. Math. Nachr. 226 (2001), 99-128. pdf

2000

13. D. Hug. Contact distributions of Boolean models. Rend. Circ. Mat. Palermo (2) Suppl. No. 65, part I (2000), 137--181. pdf

12. D. Hug and G. Last. On support measures in Minkowski spaces and contact distributions in stochastic geometry. Ann. Probab. 28 (2000), 796-850. pdf

11. A. Colesanti and D. Hug. Hessian measures of semi-convex functions and applications to support measures of convex bodies. Manuscripta Math. 101 (2000), 209-238. pdf

10. A. Colesanti and D. Hug. Steiner type formulae and weighted measures of singularities for semi-convex functions. Trans. Amer. Math. Soc. 352 (2000), 3239-3263. pdf

1999

9. D. Hug. Measures, curvatures and currents in convex geometry. Habilitationsschrift, Albert-Ludwigs-Universität Freiburg, December 1999, 191 pp. pdf

8. D. Hug. Absolute continuity for curvature measures of convex sets II. Math. Z. 232 (1999), 437-485. pdf

1998

7. D. Hug. Absolute continuity for curvature measures of convex sets I. Math. Nachr. 195 (1998), 139-158. pdf

6. D. Hug. Generalized curvature measures and singularities of sets with positive reach. Forum Math. 10 (1998), 699-728. pdf

1996

5. D. Hug. Curvature relations and affine surface area for a general convex body and its polar. Results Math. 29 (1996), 233-248. pdf

4. D. Hug. Contributions to affine surface area. Manuscripta Math. 91 (1996), 283-301. pdf

1995

3. G. Dolzmann and D. Hug. Equality of two representations of extended affine surface area. Arch. Math. 65 (1995), 352-356. pdf

2. D. Hug. On the mean number of normals through a point in the interior of a convex body. Geom. Dedicata 55 (1995), 319-340. pdf

1994

1. D. Hug, Geometrische Maße in der affinen Konvexgeometrie. Dissertation, Freiburg, 1994, 256 pp.