Hyperbolic Volume of Manifolds with Geodesic Boundary and Orthospectra |
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Authors: | Martin Bridgeman Jeremy Kahn |
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Institution: | 1. Math Dept., Boston College, Chestnut Hill, Ma, 02167, USA 2. Math Dept., Stony Brook University, Stony Brook, NY, 11794, USA
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Abstract: | In this paper we describe a function F n : R + → R + such that for any hyperbolic n-manifold M with totally geodesic boundary ${\partial M \neq \emptyset}In this paper we describe a function F
n
: R
+ → R
+ such that for any hyperbolic n-manifold M with totally geodesic boundary ?M 1 ?{\partial M \neq \emptyset} , the volume of M is equal to the sum of the values of F
n
on the 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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Keywords: | |
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