The Horocycle Flow and the Laplacian on Hyperbolic Surfaces of Infinite Genus

被引：0
|
作者：
Omri Sarig
机构：
[1] Pennsylvania State University,Mathematics Department
[2] The Weizmann Institute of Science,undefined
来源：
Geometric and Functional Analysis | 2010年 / 19卷
关键词：
Horocycle flow; infinite genus; Ratner theory; unique ergodicity; infinite invariant measures; Primary: 37D40; 37A40; Secondary: 31C12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Consider a complete hyperbolic surface which can be partitioned into countably many pairs of pants whose boundary components have lengths less than some constant. We show that any infinite ergodic invariant Radon measure for the horocycle flow is either supported on a single horocycle associated with a cusp, or corresponds canonically to an extremal positive eigenfunction of the Laplace–Beltrami operator.
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页码：1757 / 1812
页数：55
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