Affine diameters of convex bodies -- a survey
type: Item
instance of: scholarly article
title: Affine diameters of convex bodies -- a survey
zbMATH Open document ID: 1076.52001
published in: Expositiones Mathematicae
publication date: 2005-06-13T00:00:00Z
review text: Given a convex body \(K\) in \(\mathbb{R}^{d}\), and two points \(a,b\) in the boundary of \(K\), the closed segment with endpoints \(a, b\) is an affine diameter of \(K\) if there exist two distinct parallel hyperplanes supporting \(K\) at \(a\) and \(b\), respectively. Examples of affine diameters are provided by the usual diameter, and double normals of \(K\). In this survey the author reviews basic properties of affine diameters and discusses known results and open problems regarding various topics related to this notion, e.g. characterizations of centrally symmetric convex bodies, measures of symmetry, orthogonality in linear normed spaces.
reviewed by: C. Peri
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 2175361
zbMATH Keywords: affine diameter
zbMATH Keywords: critical ratio
zbMATH Keywords: measure of symmetry
zbMATH Keywords: conjugate diameters
author: Valeriu Soltan
MaRDI profile type: Publication
full work available at URL: j.exmath.2005.01.019
OpenAlex ID: W2078735418
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DOI: 10.1016/J.EXMATH.2005.01.019
description: scientific article; zbMATH DE number 2175361