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

By A. Eskin, Maryam Mirzakhani, A. Mohammadi. 2013

310 citations recorded by the source corpus.

We prove results about orbit closures and equidistribution for the SL(2,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 [EMi2] and a certain isolation property of closed SL(2,R) invariant manifolds developed in this paper.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/018639f90e85908f8d2d07605dd129156e8c377f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. A. Zorich
2. A. Eskin
3. M. Kontsevich
4. Dawei Chen
5. G. Forni
6. Carlos Matheus
7. Martin Moeller
8. Alexander I. Bufetov

In Mathematical Physics

1. A. Zorich
2. A. Eskin
3. M. Kontsevich
4. Dawei Chen
5. G. Forni
6. Martin Moeller
7. Carlos Matheus
8. Don Zagier

Citations in the corpus

• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow (2011, background): “r] and [CaWn]. A proof of Conjecture 1 has been recently announced by A. Eskin and M. Mirzakhani [EMz]; a proof of Conjecture 2 has been recently announced by A. Eskin, M. Mirzakhani and A. Mohammadi [EMzMh]. Definition 1. An invariant suborbifold is regular if in addition to (i) and (ii) it satisfies”