Infinite curvature on typical convex surfaces
type: Item
instance of: scholarly article
title: Infinite curvature on typical convex surfaces
zbMATH Open document ID: 1269.52006
published in: Geometriae Dedicata
publication date: 2012-07-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.4652
review text: The main result of the paper settles a long-standing open problem of Zamfirescu on the curvature on typical (in the sense of Baire's first category) convex surfaces. It was already shown by \textit{T. Zamfirescu} [Math. Z. 174, 135--139 (1980; Zbl 0423.53003)] that a typical convex body has points of curvature 0 in all tangent directions almost everywhere, and typical convex bodies in the plane contain uncountable many boundary points of infinite curvature [Pac. J. Math. 131, No. 1, 191--207 (1988; Zbl 0637.52005)]. Here the author shows that in any dimension, a typical convex surface contains at least one point of infinite curvature in all tangent directions.
reviewed by: Martin Henk
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 6062586
zbMATH Keywords: Baire category
zbMATH Keywords: umbilical points
zbMATH Keywords: typical convex body
zbMATH Keywords: typical convex surfaces
author: Karim Adiprasito
MaRDI profile type: Publication
OpenAlex ID: W1982760977
arXiv ID: 1011.4652
cites work: Large curvature on typical convex surfaces
cites work: Q5502770
cites work: Q4274034
cites work: Some new results on smoothness and rotundity in normed linear spaces
cites work: Q3974575
cites work: Curvature properties of typical convex surfaces
DOI: 10.1007/S10711-011-9658-0
description: scientific article; zbMATH DE number 6062586