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Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces

- M. Mirzakhani
- Mathematics
- 12 October 2006

Weil-Petersson volumes and intersection theory on the moduli space of curves

- M. Mirzakhani
- Mathematics
- 8 March 2006

In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn,… Expand

Growth of the number of simple closed geodesics on hyperbolic surfaces

- M. Mirzakhani
- Mathematics
- 1 July 2008

Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

- M. Mirzakhani
- Mathematics
- 10 December 2010

In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g \rightarrow \infty.$ We apply these asymptotic estimates to study… Expand

Counting closed geodesics in Moduli space

- A. Eskin, M. Mirzakhani
- Mathematics
- 14 November 2008

We compute the asymptotics, as R tends to infinity, of the number of closed geodesics in Moduli space of length at most R, or equivalently the number of pseudo-Anosov elements of the mapping class… Expand

Invariant and stationary measures for the SL(2,R) action on Moduli space

- A. Eskin, M. Mirzakhani
- Mathematics
- 14 February 2013

We prove some ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular… Expand

Counting Mapping Class group orbits on hyperbolic surfaces

- M. Mirzakhani
- Mathematics
- 13 January 2016

Let $S_{g,n}$ be a surface of genus $g $ with $n$ marked points. Let $X$ be a complete hyperbolic metric on $S_{g,n}$ with $n$ cusps. Every isotopy class $[\gamma]$ of a closed curve $\gamma \in… Expand

Lattice Point Asymptotics and Volume Growth on Teichmuller space.

- J. Athreya, A. Bufetov, A. Eskin, M. Mirzakhani
- Mathematics
- 24 October 2006

We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis (Mar70) to Teichmuller space. Let X be a point in Teichmuller space, and let BR(X) be the ball of radius R centered at X (with… Expand

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

- A. Eskin, M. Mirzakhani, A. Mohammadi
- Mathematics
- 14 May 2013

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… Expand

Ergodic Theory of the Space of Measured Laminations

- E. Lindenstrauss, M. Mirzakhani
- Mathematics
- 8 July 2010

We classify locally finite invariant measures and orbit closure for the action of the mapping class group on the space of measured laminations on a surface. This classification translates to a… Expand

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