Nonexistence of curvature in most points of most convex surfaces

DOI10.1007/BF01420084zbMath0427.53002MaRDI QIDQ1136359

Tudor I. Zamfirescu

Publication date: 1980

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163457

zbMATH Keywords

curvatureconvex surfaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (7)

On two conjectures of Franz Hering about convex surfaces ⋮ On an exotic pseudo-interior in the hyperspace of convex compact sets ⋮ The curvature of most convex surfaces vanishes almost everywhere ⋮ Double normals of most convex bodies ⋮ Nondifferentiability properties of the nearest point mapping ⋮ Curvatures of typical convex bodies— the complete picture ⋮ Moderate smoothness of most Alexandrov surfaces

Cites Work

• Some new results on smoothness and rotundity in normed linear spaces
• The curvature of most convex surfaces vanishes almost everywhere
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