Das Volumen spezieller konvexer Polytope. (On the volume of special convex polytopes)
type: Item
instance of: scholarly article
title: Das Volumen spezieller konvexer Polytope. (On the volume of special convex polytopes)
zbMATH Open document ID: 0664.52008
published in: Elemente der Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141462
review text: The following problem was posed by E. Heil in 1974: Let Q be the convex hull of n line segments in \({\mathbb{R}}^ n\). Is the volume of Q not smaller than the volume of S, where S is an n-simplex defined by translates of these n line segments with one common endpoint? A positive answer to a natural generalization of this question was given by \textit{P. McMullen} with characterizations of the equality case [Math. Proc. Camb. Philos. Soc. 91, 91-97 (1982; Zbl 0481.52003)]. The present paper contains an elementary proof of the restrictions of McMullen's results to Heil's original formulation of the problem, given above.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4086435
zbMATH Keywords: quermasses of convex bodies
zbMATH Keywords: volume
zbMATH Keywords: n-simplex
author: Horst Martini
reviewed by: Horst Martini
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4086435