Decomposition method related to saturated hyperball packings

Jenő Szirmai

Decomposition method related to saturated hyperball packings

Metric Geometry 2017-09-14 v1

Authors: Jenő Szirmai

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.

Keywords

sphere packings hyperbolic geometry

Cite

@article{arxiv.1709.04369,
  title  = {Decomposition method related to saturated hyperball packings},
  author = {Jenő Szirmai},
  journal= {arXiv preprint arXiv:1709.04369},
  year   = {2017}
}

Comments

13 pages, 3 figures. arXiv admin note: text overlap with arXiv:1405.0248

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