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
  • [11] SL2(R)-DYNAMICS ON THE MODULI SPACE OF ONE-HOLED DILATION TORI
    Boulanger, Adrien
    Ghazouani, Selim
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 2024, 259 (01) : 1 - 32
  • [12] ERGODIC INVARIANT MEASURES FOR ACTIONS OF SL(2,Z)
    DANI, SG
    KEANE, M
    [J]. ANNALES DE L INSTITUT HENRI POINCARE SECTION B-CALCUL DES PROBABILITES ET STATISTIQUE, 1979, 15 (01): : 79 - 84
  • [13] Stationary measures for SL2(R)-actions on homogeneous bundles over flag varieties
    Gorodnik, Alexander
    Li, Jialun
    Sert, Cagri
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2024, 2024 (814): : 47 - 89
  • [14] SL(2, R)-invariant IIB brane actions
    Bergshoeff, Eric A.
    de Roo, Mees
    Kerstan, Sven F.
    Ortin, Tomas
    Riccioni, Fabio
    [J]. JOURNAL OF HIGH ENERGY PHYSICS, 2007, (02):
  • [15] PROJECTIVE COCYCLES OVER SL(2, R) ACTIONS: MEASURES INVARIANT UNDER THE UPPER TRIANGULAR GROUP
    Bonatti, Christian
    Eskin, Alex
    Wilkinson, Amie
    [J]. ASTERISQUE, 2020, (415) : 157 - 180
  • [16] A CATEGORICAL sl2 ACTION ON SOME MODULI SPACES OF SHEAVES
    Takahashi, Ryan
    Addington, Nicolas
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 375 (12) : 8969 - 9005
  • [17] Invariant Projective Properties Under the Action of the Lie Group SL(3;R) on RP2
    Biswas, Debapriya
    Dutta, Sandipan
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2023, 93 (02) : 301 - 314
  • [18] On Jacobian ideals invariant by a reducible sl(2,C) action
    Yu, Y
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (07) : 2759 - 2791
  • [19] An ansatz for sl2-invariant R-matrices
    Bytsko A.G.
    [J]. Journal of Mathematical Sciences, 2007, 143 (1) : 2754 - 2764
  • [20] Symmetry Preserving Discretization of SL(2,R) Invariant Equations
    Bourlioux, Anne
    Rebelo, Raphael
    Winternitz, Pavel
    [J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2008, 15 (Suppl 3) : 362 - 372
12345