Sur l'ensemble critique d'un ensemble convexe. (On the critical set of a convex set)
type: Item
instance of: scholarly article
title: Sur l'ensemble critique d'un ensemble convexe. (On the critical set of a convex set)
zbMATH Open document ID: 0632.52003
DOI: 10.1007/BF01210718
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: Define the critical set of a convex body K in a finite dimensional Euclidean space as follows: for point \(p\in K\), \(\lambda (p)= \max \{\lambda \geq 0,\quad (1+\lambda)p-\lambda K\subseteq K\},\quad \lambda (K)= \max_{p\in K} \lambda (p),\) and \(C(K)=\{q\in K: \lambda (q)=\lambda (K)\}\). C(K) is called the critical set of K. The author shows that every convex body in \({\mathbb{R}}^ n\) is the critical set of some convex body in \({\mathbb{R}}^{n+2}\).
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 4028286
zbMATH Keywords: critical set of a convex body
author: Bernard Laget
reviewed by: William J. Firey
MaRDI profile type: Publication
cites work: On critical sets of convex polyhedra
full work available at URL: https://doi.org/10.1007/bf01210718
OpenAlex ID: W2062961887
description: scientific article; zbMATH DE number 4028286