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

Belolipetsky, Mikhail; Bridgeman, Martin

doi:10.2140/agt.2022.22.1255

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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

DOI: 10.2140/agt.2022.22.1255

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

Volume 22, issue 3 (2022)