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

Mikhail Belolipetsky and Martin Bridgeman

Algebraic & Geometric Topology 22 (2022) 1255–1272
Abstract

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.

Keywords
hyperbolic volume, orthospectra
Mathematical Subject Classification
Primary: 32Q45
References
Publication
Received: 6 July 2020
Revised: 7 January 2021
Accepted: 23 February 2021
Published: 25 August 2022
Authors
Mikhail Belolipetsky
IMPA
Estrada Dona Castorina, 110
22460-320 Rio de Janeiro
Brazil
Martin Bridgeman
Department of Mathematics
Boston College
Chestnut Hill, MA, 02467
United States