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arXiv · 1709.04369

Decomposition method related to saturated hyperball packings

Jenő Szirmai
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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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Jenő Szirmai. 2017-09-12. Decomposition method related to saturated hyperball packings. https://arxiv.org/abs/1709.04369

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