Lattice Point Asymptotics and Volume Growth on Teichmuller space.

  title={Lattice Point Asymptotics and Volume Growth on Teichmuller space.},
  author={Jayadev S. Athreya and Alexander I. Bufetov and A. V. Eskin and Maryam Mirzakhani},
  journal={Duke Mathematical Journal},
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. 

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