Curvatures of typical convex bodies— the complete picture

DOI10.1090/S0002-9939-2014-12245-3zbMath1317.52007MaRDI QIDQ5496262

Rolf Schneider

Publication date: 30 January 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

generalized curvaturesBaire categoryspherical imagezero curvaturetypical convex bodyumbilicinfinite curvature

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Typical curvature behaviour of bodies of constant width ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds ⋮ Normal bundle and Almgren’s geometric inequality for singular varieties of bounded mean curvature ⋮ Moderate smoothness of most Alexandrov surfaces ⋮ Curvature measures and soap bubbles beyond convexity

Cites Work

• Infinite curvature on typical convex surfaces
• Some new results on smoothness and rotundity in normed linear spaces
• Curvature properties of typical convex surfaces
• The curvature of most convex surfaces vanishes almost everywhere
• Nonexistence of curvature in most points of most convex surfaces
• Die meisten konvexen Körper sind glatt, aber nicht zu glatt
• On the curvatures of convex bodies
• Stochastic and Integral Geometry
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