Lattice point asymptotics and volume growth on Teichmüller space

Jayadev Athreya; Alexander Bufetov; Alex Eskin; Maryam Mirzakhani

doi:10.1215/00127094-1548443

Lattice point asymptotics and volume growth on Teichmüller space

Jayadev Athreya, Alexander Bufetov, Alex Eskin, Maryam Mirzakhani

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1055-1111
Number of pages	57
Journal	Duke Mathematical Journal
Volume	161
Issue number	6
DOIs	https://doi.org/10.1215/00127094-1548443
State	Published - Apr 15 2012
Externally published	Yes

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General Mathematics

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Lattice point asymptotics and volume growth on Teichmüller space

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