INVARIANT AND STATIONARY MEASURES FOR THE SL(2, R) ACTION ON MODULI SPACE

被引：75

作者：

Eskin, Alex ^{[1
]}

Mirzakhani, Maryam ^{[2
]}

机构：

[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

PUBLICATIONS MATHEMATIQUES DE L IHES | 2018年 / 127卷 / 01期

关键词：

TEICHMULLER-CURVES; UNIPOTENT FLOWS; QUADRATIC-FORMS; ORBIT CLOSURES; VEECH SURFACES; CONTRACTION PROPERTIES; ERGODIC AVERAGES; MINIMAL SETS; RIGIDITY; BILLIARDS;

D O I：

10.1007/s10240-018-0099-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove some ergodic-theoretic rigidity properties of the action of on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of is supported on an invariant affine submanifold. The main theorems are inspired by the results of several authors on unipotent flows on homogeneous spaces, and in particular by Ratner's seminal work.

引用

页码：95 / 324

页数：230

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