Lattice point asymptotics and volume growth on Teichmüller space

Jayadev Athreya, Alexander Bufetov, Alex Eskin, Maryam Mirzakhani

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)1055-1111
Number of pages57
JournalDuke Mathematical Journal
Issue number6
StatePublished - Apr 15 2012

ASJC Scopus subject areas

  • General Mathematics


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