Lower bounds for volumes and orthospectra of hyperbolic manifolds with geodesic boundary

TL;DR

This paper establishes explicit lower bounds for the volumes and orthospectra of hyperbolic manifolds with geodesic boundary, advancing understanding of their geometric properties.

Contribution

It provides explicit estimates and bounds for orthogeodesic lengths and volumes, improving previous theoretical results with concrete numerical bounds.

Findings

Lower bound for shortest orthogeodesic length in terms of volume

Alternative derivation of volume bounds as a function of dimension

Explicit estimates for functions related to hyperbolic manifolds

Abstract

In this paper we derive explicit estimates for the functions which appear in the previous work of Bridgeman and Kahn. As a consequence, we obtain an explicit lower bound for the length of the shortest orthogeodesic in terms of the volume of a hyperbolic manifold with totally geodesic boundary. We also give an alternative derivation of a lower bound for the volumes of these manifolds as a function of the dimension.