Geodesic
Isolation, equidistribution, and orbit closures for the $\mathrm{SL}(2,\mathbb{R})$ action on moduli space
Alex Eskin1 ; Maryam Mirzakhani2 ; Amir Mohammadi3
1 University of Chicago, Chicago, IL
2 Stanford University, Stanford, CA
3 University of Texas, Austin, TX
Annals of mathematics, Tome 182 (2015) no. 2, pp. 673-721.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove results about orbit closures and equidistribution for the $\mathrm{SL}(2,\mathbb{R})$ action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure classification theorem of the first two authors and a certain isolation property of closed $\mathrm{SL}(2,\mathbb{R})$ invariant manifolds developed in this paper.
DOI : 10.4007/annals.2015.182.2.7

Alex Eskin 1 ; Maryam Mirzakhani 2 ; Amir Mohammadi 3

1 University of Chicago, Chicago, IL
2 Stanford University, Stanford, CA
3 University of Texas, Austin, TX 
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Alex Eskin; Maryam Mirzakhani; Amir Mohammadi. Isolation, equidistribution, and orbit closures for the $\mathrm{SL}(2,\mathbb{R})$ action on  moduli space. Annals of mathematics, Tome 182 (2015) no. 2, pp. 673-721. doi : 10.4007/annals.2015.182.2.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.2.7/

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