## Duke Mathematical Journal

### Lattice point asymptotics and volume growth on Teichmüller space

#### Abstract

We apply some of the ideas of Margulis’s Ph.D. dissertation to Teichmüller space. Let $X$ be a point in Teichmüller space, and let $B_{R}(X)$ 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 $B_{R}(X)$, and also for the cardinality of the intersection of $B_{R}(X)$ with an orbit of the mapping class group.

#### Article information

Source
Duke Math. J. Volume 161, Number 6 (2012), 1055-1111.

Dates
First available in Project Euclid: 5 April 2012

http://projecteuclid.org/euclid.dmj/1333633316

Digital Object Identifier
doi:10.1215/00127094-1548443

Mathematical Reviews number (MathSciNet)
MR2913101

Zentralblatt MATH identifier
1246.37009

Subjects
Primary: 37A25: Ergodicity, mixing, rates of mixing

#### Citation

Athreya, Jayadev; Bufetov, Alexander; Eskin, Alex; Mirzakhani, Maryam. Lattice point asymptotics and volume growth on Teichmüller space. Duke Math. J. 161 (2012), no. 6, 1055--1111. doi:10.1215/00127094-1548443. http://projecteuclid.org/euclid.dmj/1333633316.

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