Lower bounds for the volume of hyperbolic $n$-orbifolds

TL;DR

This paper derives an explicit lower bound formula for the volume of hyperbolic orbifolds, depending on their dimension and torsion properties, advancing understanding of their geometric constraints.

Contribution

It introduces a new explicit volume lower bound formula for hyperbolic orbifolds based on dimension and torsion order, which was not previously available.

Findings

Derived a formula for volume lower bounds of hyperbolic orbifolds.

The bound depends explicitly on dimension and torsion order.

Provides a tool for estimating minimal orbifold volumes in hyperbolic geometry.

Abstract

In this paper an explicit formula for a lower bound on the volume of a hyperbolic orbifold, dependent on dimension and the maximal order of torsion in the orbifolds' fundamental group, is constructed.