Densest packing of equal spheres in hyperbolic space
type: Item
instance of: scholarly article
title: Densest packing of equal spheres in hyperbolic space
zbMATH Open document ID: 1018.52016
author: Charles Radin
author: Lewis Bowen
published in: Discrete \& Computational Geometry
publication date: 2003-03-17T00:00:00Z
review text: In hyperbolic space the definition of ``densest packing of equal spheres'' poses problems (not encountered in Euclidean space). The authors put some order into this complex situation: they show that there is a natural meaning for ``optimally dense'' packings in hyperbolic space. Furthermore, they show that only for a special countable set of radii values \(R\) do congruent balls of radius \(R\) have optimally dense packing with high symmetry (again in contrast to Euclidean space). They associate to a packing \(x\) an invariant measure \(\mu_x\) on a space of packings and define an average density \(D(\mu_x)\) to such a measure. This cannot be done for every packing since there are packing examples given by \textit{K. Böröczky} [Mat. Lapok 25(1974), 265-306 (1977; Zbl 0394.52012)] and \textit{G. Fejes Tóth} and \textit{W. Kuperberg} [in Handbook of convex geometry. Vol. B, 799-860 (1993; Zbl 0789.52018)] that have no well-defined density. This paper has a fine bibliography, a survey-type presentation and a (possibly) seminal future.
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 1883353
zbMATH Keywords: densest packing of equal spheres
zbMATH Keywords: hyperbolic space
MaRDI profile type: Publication
full work available at URL: s00454-002-2791-7
OpenAlex ID: W2161660300
Wikidata QID: Q56267766
DOI: 10.1007/S00454-002-2791-7
description: scientific article; zbMATH DE number 1883353