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
收藏
页码：95 / 324
页数：230
相关论文
共 50 条
  • [31] Classification of left-invariant Einstein metrics on SL(2, R) x SL(2, R) that are bi-invariant under a one-parameter subgroup
    Cortes, Vicente
    Ehlert, Jeremias
    Haupt, Alexander S.
    Lindemann, David
    [J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2023, 63 (02)
  • [32] Moduli space of bi-invariant metrics
    Torres, Juan Flores
    [J]. BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2024, 30 (02):
  • [33] Symplectic and isometric SL(2, R)-invariant subbundles of the Hodge bundle
    Avila, Artur
    Eskin, Alex
    Moeller, Martin
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 732 : 1 - 20
  • [34] On naturally reductive left-invariant metrics of SL(2, R)
    Halverscheid, Stefan
    Iannuzzi, Andrea
    [J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2006, 5 (02) : 171 - 187
  • [35] Coupling-constant metamorphosis in SL(2, R)-invariant systems
    Masterov, Ivan
    Masterova, Maria
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2021, 168
  • [36] On constant Uq(sl2)-invariant R-matrices
    Bytsko A.G.
    [J]. Journal of Mathematical Sciences, 2010, 168 (6) : 805 - 810
  • [37] ON THE SUPPORT OF ABSOLUTELY CONTINUOUS GAUSS MEASURES ON SL(2,R)
    MCCRUDDEN, M
    WOOD, RM
    [J]. LECTURE NOTES IN MATHEMATICS, 1984, 1064 : 379 - 397
  • [38] Stationary measures and closed invariant of homogenous spaces
    Benoist, Yves
    Quint, Jean-Francois
    [J]. ANNALS OF MATHEMATICS, 2011, 174 (02) : 1111 - 1162
  • [39] SUPPORT OF R!- INVARIANT MEASURES
    TSERPES, NA
    MUKHERJE.A
    [J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1970, 270 (13): : 816 - &
  • [40] Stationary measures and invariant subsets of homogeneous spaces
    Benoist, Yves
    Quint, Jean-Frangois
    [J]. COMPTES RENDUS MATHEMATIQUE, 2009, 347 (1-2) : 9 - 13
12345