Limit sets of discrete groups of isometries of exotic hyperbolic spaces
Limit sets of discrete groups of isometries of exotic hyperbolic spaces
复制标题
奇异双曲空间等距离散群的极限集
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Iozzi
中科院分区：
文献类型：
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作者：
K. Corlette;A. Iozzi
设Γ是双曲空间HF的几何有限离散等距群，其中F = R，C，H或O（此时n = 2）.我们证明了Γ的临界指数等于极限集Λ（Γ）的Hausdorff维数，且作用在平方可积函数上的Laplacian的最小特征值是它们之一的二次函数（当它们足够大时）.证明了测地线流关于Bowen-Margulis测度的Hopf遍历性定理的一个推广。
Let Γ be a geometrically finite discrete group of isometries of hyperbolic space HF , where F = R, C, H or O (in which case n = 2). We prove that the critical exponent of Γ equals the Hausdorff dimension of the limit sets Λ(Γ) and that the smallest eigenvalue of the Laplacian acting on square integrable functions is a quadratic function of either of them (when they are sufficiently large). A generalization of Hopf ergodicity theorem for the geodesic flow with respect to the Bowen-Margulis measure is also proven.