Hyperbolic volume of n-manifolds with geodesic boundary and orthospectra

2010/02/09 by Martin Bridgeman, Bridgeman, Martin, Jeremy Kahn +1
Computer Science · Engineering · Mathematics · #32Q45 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #Metric Geometry (math.MG) #math.FA #math.MG #msc:32Q45

paper · pdf · doi:10.48550/arxiv.1002.1905

19 pages, 3 figures

arxiv created 2010/02/09 · openalex publication_date 2010/02/09 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe a function F_n:\bf R₊ → \bf R₊ such that for any hyperbolic n-manifold M with totally geodesic boundary ∂ M ≠ ∅, the volume of M is equal to the sum of the values of F_n on the \em orthospectrum of M. We derive an integral formula for F_n in terms of elementary functions. We use this to give a lower bound for the volume of a hyperbolic n-manifold with totally geodesic boundary in terms of the area of the boundary.

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