Publications mathématiques de l'IHÉS

, Volume 127, Issue 1, pp 95–324 | Cite as

Invariant and stationary measures for the Open image in new window action on Moduli space

  • Alex Eskin
  • Maryam Mirzakhani


We prove some ergodic-theoretic rigidity properties of the action of Open image in new window on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of Open image in new window 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.


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© IHES and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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