Counting curves in hyperbolic surfaces

Viveka Erlandsson, Juan Souto

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract. LetΣbeahyperbolic surface.Westudythe setofcurveson Σofagiven type, i.e. in the mapping class group orbit of some fixed but otherwise arbitrary γ0. For example, in the particular case that Σ is a once-punctured torus, we prove that the cardinality of the set of curves of type γ0 and of at most length L is asymptotic to L2 times a constant.
Original languageEnglish
Pages (from-to)729-777
JournalGeometric and Functional Analysis
Publication statusPublished - 18 Jul 2016

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