Prof. em. Dr. Dr. h.c. Rolf Schneider
Mathematisches Institut
Albert-Ludwigs-Universität
Ernst-Zermelo-Str. 1
D-79104 Freiburg i. Br.
email: rolf.schneider@math.uni-freiburg.de

Second expanded edition
Research interests: Convex geometry,
integral
geometry,
stochastic
geometry
Preprints:
- Rolf Schneider: Minkowski type theorems for convex sets in
cones. arXiv:2008.07248 Acta Math. Hungar. (accepted)
pdf
- Daniel Hug and Rolf Schneider: Threshold phenomena for random
cones. arXiv:2004.11473v1 (submitted) pdf
- Rolf
Schneider: The polytopes in a Poisson hyperplane
tessellation. arXiv:1804.05622v1
Proc. Amer. Math. Soc. (accepted) pdf
Publications of the last five years:
- Rolf Schneider: Random Gale diagrams and neighborly polytopes in
high dimensions. Beitr. Algebra Geom.
doi.org/10.1007/s13366-020.00526-3 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.115 (2020), 339-351.
DOI
10.1007/s00013-020-01465-0 pdf
- Daniel Hug and Rolf Schneider: Poisson hyperplane processes and
approximation of convex bodies.
Mathematika 66 (2020),
713-732.
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
List of publications: pdf
Errata
for
"Convex
Bodies - the Brunn-Minkowski Theory" (Second edition)
Errata
for "Stochastic and Integral Geometry"
Errata for
"Convex
Bodies - the Brunn-Minkowski Theory" (First edition)
Course Materials:
- 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