Lattice Point Asymptotics and Volume Growth on Teichmüller Space
Résumé
We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis [Mar70] to Teichmüller space. Let X be a point in Teichmüller space, and let BR(X) be the ball of radius R centered at X (with distances measured in the Teichmüller 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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