Abstract
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 those packings to be considered optimally dense. 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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Bowen, L., Radin, C. Optimally Dense Packings of Hyperbolic Space. Geometriae Dedicata 104, 37–59 (2004). https://doi.org/10.1023/B:GEOM.0000022857.62695.15
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DOI: https://doi.org/10.1023/B:GEOM.0000022857.62695.15