Counting curves in hyperbolic surfaces

Viveca Erlandsson, Juan Souto*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

Let Σ be a hyperbolic surface. We study the set of curves on Σ of a given 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
Number of pages48
JournalGEOMETRIC AND FUNCTIONAL ANALYSIS
Volume26
Issue number3
DOIs
Publication statusPublished - 2016
MoE publication typeA1 Journal article-refereed

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