Lattice Point Asymptotics and Volume Growth on Teichmuller space.

By Jayadev S. Athreya, Alexander I. Bufetov, A. Eskin, Maryam Mirzakhani. 2006

90 citations recorded by the source corpus.

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 distances measured in the Teichmuller metric). We obtain asymptotic formulas as R tends to infinity for the volume of BR(X), and also for the cardinality of the intersection of BR(X) with an orbit of the mapping class group.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/66951e41a9bff16e2c0cd5c6bbb4d6eb41dd38da

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow (2010, methodology): “A similar construction is given in [ABEM06, Section 2], in more geometric terms.”
Statistically convex-cocompact actions of groups with contracting elements (2016, background): “oups of compact rank-1 manifolds by G. Kneiper [53], (4)Relatively hyperbolic groups for word metric [87], hyperbolic metric [90], (5)Mapping class groups for Teichmuller metric by J. Athreya et al. [5]. Lets brie y comment on the last item. In fact, our general argument works for mapping class grou”
A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle (2010, background): “The Hodge Riemannian metrics have been explicitly constructed and studied in depth in [1].”