Density of tube packings in hyperbolic space
type: Item
instance of: scholarly article
title: Density of tube packings in hyperbolic space
zbMATH Open document ID: 1092.51004
author: Andrew Przeworski
published in: Pacific Journal of Mathematics
publication date: 2005-02-16T00:00:00Z
review text: The motivation of this topic has been the Euclidean result of \textit{A. Bezdek} and \textit{W. Kuperberg} [Mathematika 37, No. 1, 74--80 (1990; Zbl 0715.52006)] proving the same optimal density \(\pi/\sqrt {12}\) as that of Euclidean plane packing of equal circles. In hyperbolic space \(H^3\), there is a result of \textit{T. H. Marshall} and \textit{G. J. Martin} [Ann. Acad. Sci. Fenn., Math. 30, No. 1, 3--48 (2005; Zbl 1079.52011)], providing an upper bound for very large radius tubes which is asymptotically sharp. The author's results refer to moderate radius tubes where the packing has a symmetry group of \(H^3\). Thus the density can be considered in a hyperbolic manifold of finite volume. Seemingly, the author intensively works in this field which promises further results.
reviewed by: Emil Molnár
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 52A55
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 2134759
zbMATH Keywords: density in manifold
MaRDI profile type: Publication
OpenAlex ID: W2081717968
DOI: 10.2140/PJM.2004.214.127
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description: scientific article; zbMATH DE number 2134759