Counting curves in hyperbolic surfaces

Research output: Contribution to journalArticleScientificpeer-review

Researchers

  • Viveca Erlandsson
  • Juan Souto

Research units

  • Université de Rennes 1

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.

Details

Original languageEnglish
Pages (from-to)729–777
Number of pages48
JournalGEOMETRIC AND FUNCTIONAL ANALYSIS
Volume26
Issue number3
Publication statusPublished - 2016
MoE publication typeA1 Journal article-refereed

ID: 6749017