Inequalities for volumes of simplices in terms of their faces
type: Item
instance of: scholarly article
title: Inequalities for volumes of simplices in terms of their faces
zbMATH Open document ID: 0917.51023
DOI: 10.1023/A:1005044929055
author: V. Volenec
author: Darko Veljan
author: J. Pečarić
published in: Geometriae Dedicata
publication date: 1999-08-02T00:00:00Z
review text: The authors generalize some known geometric inequalities referring to \(n\)-dimensional simplicies in Euclidean \(n\)-space, \(n\geq 2\). More precisely, they obtain an inequality involving the volume and the product of \(k\)-volumes of \(k\)-dimensional faces of an \(n\)-simplex, \(k\in\{1,2, \dots, n\}\). On that basis, they derive generalizations of two inequalities maximizing the volume of one or two \(n\)-simplicies in terms of their edge lengths. The obtained inequalities yield also (in form of the equality cases) characterizations of regular \(n\)-simplices.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 51M16
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 1240987
zbMATH Keywords: simplex
zbMATH Keywords: regular simplex
zbMATH Keywords: geometric inequality
zbMATH Keywords: volume
MaRDI profile type: Publication
full work available at URL: a:1005044929055
OpenAlex ID: W104103229
description: scientific article; zbMATH DE number 1240987