The least dense hyperball covering to the regular prism tilings in the hyperbolic $n$-space

TL;DR

This paper investigates the least dense arrangements of hyperballs that cover regular prism tilings in hyperbolic n-space, complementing previous work on densest packings.

Contribution

It introduces the dual problem of covering in hyperbolic space and determines the least dense hyperball configurations for regular prism tilings.

Findings

Identified the least dense hyperball coverings for regular prism tilings.

Calculated the densities of these coverings.

Extended the understanding of hyperball arrangements in hyperbolic geometry.

Abstract

After having investigated the densest packings by congruent hyperballs to the regular prism tilings in the $n$-dimensional hyperbolic space $\mathbb{H}^n$ ($n \in \mathbb{N}, n \ge 3)$ we consider the dual covering problems and determine the least dense hyperball arrangements and their densities.