The Kneser-Poulsen conjecture for spherical polytopes
type: Item
instance of: scholarly article
title: The Kneser-Poulsen conjecture for spherical polytopes
zbMATH Open document ID: 1059.52016
author: Károly Bezdek
author: Robert Connelly
published in: Discrete \& Computational Geometry
publication date: 2004-12-16T00:00:00Z
review text: The authors prove the following result and some related statements: If a finite set of balls of radius \(\frac{\pi}{2}\) in the unit sphere \(S^n\) of Euclidean \((n+1)\)-space is rearranged so that the distance between each pair of centers does not decrease, then the (spherical) volume of the intersection does not increase, and the (spherical) volume of the union does not decrease. This can be considered as a spherical analogue of the Kneser-Poulsen conjecture for radii all equal to \(\frac{\pi}{2}\).
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 2123183
zbMATH Keywords: Schläfli differential form
zbMATH Keywords: sphere packing
zbMATH Keywords: ball packing
zbMATH Keywords: space of constant curvature
Wikidata QID: Q122981901
MaRDI profile type: Publication
full work available at URL: s00454-004-0831-1
OpenAlex ID: W1999457828
DOI: 10.1007/S00454-004-0831-1
description: scientific article; zbMATH DE number 2123183