Hyperbolic volume of n-manifolds with geodesic boundary and orthospectra

Abstract

In this paper we describe a function $F_n:{\mathbf{R}}_{+}\to {\mathbf{R}}_{+}$ such that for any hyperbolic n-manifold $M$ with totally geodesic boundary $\partial M\ne \varnothing$, 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.

19 pages, 3 figures

References in corpus (1)

• Minimum volume cusped hyperbolic three-manifolds