Hedgehog theory and polytopes
type: Item
instance of: scholarly article
title: Hedgehog theory and polytopes
zbMATH Open document ID: 1053.52009
DOI: 10.1016/S1631-073X(03)00020-7
author: Yves Martinez-Maure
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-01-01T00:00:00Z
review text: Hedgehogs are hyperfaces which describe differences of convex bodies (with \(C^2\) support functions). Here, the author extends this notion to arbitrary differences of convex bodies (support functions) by defining a hedgehog inductively as a collection of lower-dimensional support sets. He then introduces the notion of (weak and strong) hyperbolicity of polytopal hedgehogs in \(\mathbb{R}^3\) and shows that such hedgehogs exist.
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52B10
zbMATH DE Number: 1907768
zbMATH Keywords: hedgehogs
zbMATH Keywords: differences of convex bodies
zbMATH Keywords: polytopes
zbMATH Keywords: hyperbolicity
reviewed by: Wolfgang Weil
MaRDI profile type: Publication
cites work: On the regularity of the solution of then-dimensional Minkowski problem
cites work: Q3806286
cites work: Hedgehogs and zonoids
cites work: A counter-example to a conjectured characterization of the sphere
cites work: Q4436190
full work available at URL: s1631-073x(03)00020-7
OpenAlex ID: W2035112828
description: scientific article; zbMATH DE number 1907768