Counting curves in hyperbolic surfaces

Viveca Erlandsson; Juan Souto

doi:10.1007/s00039-016-0374-7

Counting curves in hyperbolic surfaces

Viveca Erlandsson, Juan Souto^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	729–777
Number of pages	48
Journal	GEOMETRIC AND FUNCTIONAL ANALYSIS
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/s00039-016-0374-7
Publication status	Published - 2016
MoE publication type	A1 Journal article-refereed

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