On volumes of hyperbolic orbifolds

TL;DR

This paper establishes an explicit lower bound on the volume of hyperbolic n-orbifolds for dimensions four and above, using Wang's bound on embedded ball radii in fundamental domains.

Contribution

It provides a new explicit lower volume bound for hyperbolic orbifolds in higher dimensions, extending previous theoretical results.

Findings

Derived explicit lower volume bounds for hyperbolic orbifolds

Applied Wang's radius bound to fundamental domains

Enhanced understanding of geometric properties of hyperbolic orbifolds

Abstract

In this paper we derive an explicit lower bound on the volume of a hyperbolic $n$-orbifold for dimensions greater than or equal to four. Our main tool is H. C. Wang's bound on the radius of a ball embedded in the fundamental domain of a discrete subgroup of a semisimple Lie group.