Hyperbolic Volume of Manifolds with Geodesic Boundary and Orthospectra
Hyperbolic Volume of Manifolds with Geodesic Boundary and Orthospectra
复制标题
具有测地线边界和正交谱的流形的双曲体积
DOI：
10.1007/s00039-010-0095-2
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发表时间：
2010
影响因子：
2.2
通讯作者：
Jeremy A. Kahn
中科院分区：
文献类型：
--
作者：
M. Bridgeman;Jeremy A. Kahn
本文描述了一个函数Fn：R+ → R+，使得对任意具有全测地边界的双曲n-流形M，M的体积等于Fn在M的正交谱上的值之和.我们用初等函数导出了Fn的积分公式。我们利用这一点给出了一个双曲n-流形的体积与全测地边界的边界面积的下界。
In this paper we describe a function Fn : R+ → 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 Fn on the orthospectrum of M. We derive an integral formula for Fn 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.