Duke Mathematical Journal

Lattice point asymptotics and volume growth on Teichmüller space

Jayadev Athreya, Alexander Bufetov, Alex Eskin, and Maryam Mirzakhani

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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 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.

Article information

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

First available in Project Euclid: 5 April 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37A25: Ergodicity, mixing, rates of mixing
Secondary: 30F60: Teichmüller theory [See also 32G15]


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

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