Isolation, equidistribution, and orbit closures for the SL(2,R) action\n on Moduli space

2013/05/14 by Alex Eskin, Eskin, Alex, Maryam Mirzakhani +3 · 8 citations
Mathematics · #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1305.3015

Abstract

We prove results about orbit closures and equidistribution for the SL(2,R)\naction on the moduli space of compact Riemann surfaces, which are analogous to\nthe theory of unipotent flows. The proofs of the main theorems rely on the\nmeasure classification theorem of [EMi2] and a certain isolation property of\nclosed SL(2,R) invariant manifolds developed in this paper.\n

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