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arXiv 1002.19052010-02-09math.MGmath.FA

Hyperbolic volume of n-manifolds with geodesic boundary and orthospectra

Martin Bridgeman, Jeremy Kahn

备注：: 19 pages, 3 figures

英文摘要：

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