Decomposition method related to saturated hyperball packings

2017/09/12 by Szirmai, Jenő · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1709.04369

Abstract

In this paper we study the problem of hyperball (hypersphere) packings in 3-dimensional hyperbolic space. We introduce a new definition of the non-compact saturated ball packings and describe to each saturated hyperball packing, a new procedure to get a decomposition of 3-dimensional hyperbolic space \HYP into truncated tetrahedra. Therefore, in order to get a density upper bound for hyperball packings, it is sufficient to determine the density upper bound of hyperball packings in truncated simplices.

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• Decomposition method and upper bound density related to congruent saturated hyperball packings in hyperbolic n-space

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