Optimally dense packings of hyperbolic space

Details Optimally dense packings of hyperbolic space Optimally dense packings of hyperbolic space

2002-11-26

arxiv.org/abs/math/0211417v1

Mathematics

Metric Geometry

27 pages, 11 figures

Scientific paper

In previous work a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an appropriate definition of optimal dense packings. Examples are given to illustrate various aspects of the density problem, in particular the shift in emphasis from the analysis of individual packings to spaces of packings.

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