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: Random Gale diagrams and neighborly polytopes in high dimensions. arXiv:2006.02156v1 (submitted)  pdf
• Daniel Hug and Rolf Schneider: Threshold phenomena for random cones. arXiv:2004.11473v1 (submitted)  pdf
• Daniel Hug and Rolf Schneider: Poisson hyperplane processes and approximation of convex bodies. arXiv:1908.09498v1 Mathematika  (accepted).  pdf
• Rolf Schneider: The polytopes in a Poisson hyperplane tessellation. arXiv:1804.05622v1  Proc. Amer. Math. Soc. (accepted)  pdf

• Rolf Schneider: Separation bodies: a conceptual dual to floating bodies. Monatsh. Math. 193 (2020), 157-170. DOI 10.1007/s00605-020-01443-2   pdf
• Daniel Hug and Rolf Schneider: Integral geometry of pairs of hyperplanes and lines. Arch. Math. DOI 10.1007/s00013-020-01465-0  pdf
• Rolf Schneider: Interaction of Poisson hyperplane processes and convex bodies.  J. Appl. Prob. 56 (2019), 1020-1032.  pdf
• Rolf Schneider: On a formula for the volume of polytopes. In: Geometric Aspects of Functional Analysis (Israel Seminar 2017-2019), vol. II, pp. 335-345, Lecture Notes Math. 2266, Springer, 2020.    pdf
• Rolf Schneider: Small faces in stationary Poisson hyperplane tessellations. Math. Nachr. 292 (2019), 1811-1822.  pdf
• Rolf Schneider: Conic support measures. J. Math. Anal. Appl. 471 (2019), 812-825  pdf
• Rolf Schneider: Polyhedral Gauss-Bonnet theorems and valuations. Beiträge Algebra Geom. 59 (2018), 199-210.  pdf
• Rolf Schneider: A Brunn-Minkowski theory for coconvex sets of finite volume. Adv. Math. 332 (2018), 199-234.    pdf 
• Rolf Schneider: Intersection probabilities and kinematic formulas for polyhedral cones. Acta Math. Hungar.  155 (2018), 3-24.   pdf
• Rolf Schneider: The typical irregularity of virtual convex bodies. J. Convex Anal. 25 (2018), 103-118.  pdf
• Matthias Reitzner and Rolf Schneider: On the cells in a stationary Poisson hyperplane mosaic. Adv. Geom. 19 (2019), 145-150.  pdf
• Rolf Schneider: Combinatorial identities for polyhedral cones. St. Petersburg Math. J.  29 (2018), 209-221.  pdf
• Rolf Schneider: The middle hedgehog of a planar convex body. Beitr. Algebra Geom. 58 (2017), 235-245.   pdf
• Daniel Hug and Rolf Schneider: Rotation covariant local tensor valuations on convex bodies. Commun. Contemp. Math. 19, no. 5, 1650061 (2017), 31 pp. pdf
• Daniel Hug and Rolf Schneider: SO(n) covariant local tensor valuations on polytopes. Michigan Math. J. 66 (2017), 637--659  pdf
• José Pedro Moreno and Rolf Schneider: Multiplication of convex sets in C(K) spaces. Studia Math. 232 (2016), 173-187.   pdf
• Rolf Schneider: Discrete aspects of stochastic geometry. In Handbook of Discrete and Computational Geometry, 3rd edn., (J.E. Goodman, J. O'Rourke, C.D.Tóth, eds.), pp 299-329, CRC Press, Boca Raton, 2018.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, Daniel Hug and Rolf Schneider: Affine diameters of convex bodies. Proc. Amer. Math. Soc. 144 (2016), 797-812.   pdf
• Dan Florentin, Vitali Milman and Rolf Schneider: A characterization of the mixed discriminant. Proc. Amer. Math. Soc. 144 (2016), 2197-2204.   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
• Convex Cones. (Summer School "New Perspectives on Convex Geometry", Castro Urdiales, September 3 - 7, 2018).  pdf