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Invariant and stationary measures for the action on Moduli space
Authors:Alex Eskin  Maryam Mirzakhani
Institution:1.Department of Mathematics,University of Chicago,Chicago,USA;2.Department of Mathematics,Stanford University,Stanford,USA
Abstract:We prove some ergodic-theoretic rigidity properties of the action of Open image in new window /></a> </span> on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of <span class= Open image in new window /></a> </span> 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.</td>
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