Ball packings in hyperbolic space

TL;DR

This paper explores the challenges of defining and analyzing sphere packings in hyperbolic space, focusing on local density bounds and the concept of optimal arrangements in this non-Euclidean setting.

Contribution

It introduces methods to describe local density bounds and discusses various approaches to defining optimal packings in hyperbolic space.

Findings

Local density bounds for hyperbolic sphere packings established

Discussion of different approaches to defining optimal arrangements

Insights into the limitations of Euclidean concepts in hyperbolic geometry

Abstract

In hyperbolic space density cannot be defined by a limit as we define it in Euclidean space. We describe the local density bounds for sphere packings and we discuss the different attempts to define optimal arrangements in hyperbolic space.