Albert-Ludwigs-Universität Freiburg Mathematisches Institut Arbeitsgruppe Geometrie

Prof. em. Dr. Dr. h.c. Rolf Schneider

Mathematisches Institut

email: rolf.schneider@math.uni-freiburg.de

• Rolf Schneider: Polyhedral Gauss-Bonnet theorems and valuations. (submitted)  pdf
• Rolf Schneider: A Brunn-Minkowski theory for coconvex sets of finite volume. (submitted)  pdf
• Rolf Schneider: Intersection probabilities and kinematic formulas for polyhedral cones. (submitted) pdf
• Rolf Schneider: The typical irregularity of virtual convex bodies. J. Convex Anal. (accepted)  pdf
• Matthias Reitzner and Rolf Schneider: On the cells in a stationary Poisson hyperplane mosaic. Adv. Geom. (accepted)  pdf
• Rolf Schneider: Combinatorial identities for polyhedral cones. St. Petersburg Math. J. (accepted)  pdf
• Daniel Hug and Rolf Schneider: Rotation covariant local tensor valuations on convex bodies. Commun. Contemp. Math. (accepted)  pdf
• Daniel Hug and Rolf Schneider: SO(n) covariant local tensor valuations on polytopes. Michigan Math. J. (accepted)  pdf
• Rolf Schneider: Discrete aspects of stochastic geometry. (Handbook article, 3rd updated version)  pdf

• Rolf Schneider: The middle hedgehog of a planar convex body. Beitr. Algebra Geom. 58 (2017), 235-245.   pdf
• José Pedro Moreno and Rolf Schneider: Multiplication of convex sets in C(K) spaces. Studia Math. 232 (2016), 173-187.   pdf
• Daniel Hug and Rolf Schneider: Random conical tessellations. Discrete Comput. Geom. 56 (2016) 395--426.  pdf
• Daniel Hug and Rolf Schneider: Tensor valuations and their local versions.  In: Tensor Valuations and Their Applications in Stochastic Geometry and Imaging (E.B. Vedel Jensen, M. Kiderlen, eds), pp. 27-65, Lecture Notes in Math., vol. 2177, Springer, 2017.  pdf
• Rolf Schneider: Valuations on convex bodies - the classical basic facts. In: Tensor Valuations and Their Applications in Stochastic Geometry and Imaging (E.B. Vedel Jensen, M. Kiderlen, eds), pp. 1-25, Lecture Notes in Math., vol. 2177, Springer, 2017.  pdf
• Imre Bárány, Daniel Hug, Matthias Reitzner  and Rolf Schneider: Random points in halfspheres. Random Structures Algorithms 50 (2017), 3-22.  pdf
• Rolf Schneider: Second moments related to Poisson hyperplane tessellations. J. Math. Anal. Appl. 434 (2016), 1365-1375. pdf 
• Rolf Schneider: Reflections of planar convex bodies. In Convexity and Discrete Geometry Including Graph Theory, Mulhouse, France, September 2014 (K. Adiprasito, I. Bárány, C. Vilcu, eds.), pp. 69-76, Springer, 2016.   pdf
• Imre Bárány  and Rolf Schneider: Typical curvature behaviour of bodies of constant width. Adv. Math. 272 (2015), 308-329. doi: 10.1016/j.aim.2014.10.025  pdf
• Imre Bárány, Daniel Hug and Rolf Schneider: Affine diameters of convex bodies. Proc. Amer. Math. Soc. 144 (2016), 797-812.   pdf
• Rolf Schneider: A formula for mixed volumes.  In Geometric Aspects of Functional Analysis (Israel Seminar 2011-2013), pp. 423-426, Lecture Notes Math. 2116, Springer,  2014.  pdf
• José Pedro Moreno and Rolf Schneider: Some geometry of convex bodies in C(K) spaces. J. Math. Pures Appl. 103 (2015), 352-373.  http://dx.doi.org/10.1016/j.matpur.2014.04.007  pdf
• Daniel Hug and Rolf Schneider: Hölder continuity for support measures of convex bodies. Arch Math. 104 (2015), 83-92.   pdf
• Daniel Hug and Rolf Schneider: Local tensor valuations. Geom. Funct. Anal. 24 (2014), 1516-1564. DOI: 10.1007/s00039-014-0289-0  pdf
• Dan Florentin, Vitali Milman and Rolf Schneider: A characterization of the mixed discriminant. Proc. Amer. Math. Soc. 144 (2016), 2197-2204.   pdf
• Rolf  Schneider: Curvatures of typical convex bodies  - The complete picture. Proc. Amer. Math. Soc. 143 (2015), 387-393. pdf
• Rolf Schneider: Affine surface area and convex bodies of elliptic type. Periodica Math. Hungar.  69 (2014), 120-125. DOI 10.1007/s10998-014-0050-3  pdf
• José Pedro Moreno and Rolf Schneider: Lipschitz selections of the diametric completion mapping in Minkowski spaces.  Adv. Math. 233 (2013), 248-267.  pdf
• Daniel Hug and Rolf Schneider: Approximation properties of random polytopes associated with Poisson hyperplane processes. Adv. Appl. Prob.  46 (2014), 919-936.   arXiv:1309.3989   pdf
• Imre Bárány and Rolf Schneider: Universal points of convex bodies and bisectors in Minkowski spaces. Adv. Geom. 14 (2014), 427-445.   pdf
• Rolf Schneider: Local tensor valuations on  convex polytopes. Monatsh. Math. 171 (2013), 459-479.  pdf
• José Pedro Moreno and Rolf Schneider: Structure of the space of diametrically complete sets in a Minkowski space. Discrete Comput. Geom.  48 (2012), 467-486.  SpringerLink   pdf 
• José Pedro Moreno and Rolf Schneider: Diametrically complete sets in Minkowski spaces. Israel. J. Math. 191 (2012), 701-720.  pdf
• José Pedro Moreno and Rolf Schneider:  Local Lipschitz continuity of the diametric completion mapping. Houston J. Math. 38 (2012), 1207-1223. pdf
• Rolf Schneider: Extremal properties of random mosaics.  In Geometry - Intuitive, Discrete, and Convex. A Tribute to László Fejes Tóth  (I. Bárány, K. J. Böröczky, G. Fejes Tóth, J. Pach, eds), Bolyai Soc. Math. Studies 24, pp. 301-330, Springer, Berlin, 2013.  pdf

• Integral Geometry - Measure Theoretic Approach and Stochastic Applications (part of  an Advanced Course on Integral Geometry, Centre de Recerca Matemàtica, Bellaterra (Spain); September 15 - 23, 1999. Quaderns núm. 16 (1999), 159 - 227)  pdf
  
• Convexity and Geometric Probabilities (Lecture Series, University of Heraklion, Crete, March - April, 2001)  pdf
  
• Integral Geometric Tools for Stochastic Geometry  (part of a C.I.M.E. Summer School on Stochastic Geometry, Martina Franca, September 13 - 18, 2004) pdf
• Convexity in Stochastic Geometry (part of a Winter School on Probabilistic Methods in High Dimensions, Toulouse, January 10 - 14, 2005) pdf
• Simplices (Educational talks in the Research Semester on Geometric Methods in Analysis and Probability, Erwin Schrödinger Institute, Vienna, July 2005) pdf
• The use of spherical harmonics in convex geometry (Summer school on  "Fourier analytic and probabilistic methods in geometric functional analysis and convexity", Kent State University, August 13-20, 2008)  pdf