Counting curves in hyperbolic surfaces

Viveka Erlandsson; Juan Souto

doi:10.1007/s00039-016-0374-7

Counting curves in hyperbolic surfaces

Viveka Erlandsson
, Juan Souto

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

30 Citations (Scopus)

350 Downloads (Pure)

Abstract

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 language	English
Pages (from-to)	729-777
Journal	Geometric and Functional Analysis
Volume	26
DOIs	https://doi.org/10.1007/s00039-016-0374-7
Publication status	Published - 18 Jul 2016

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Dr Viveka Erlandsson
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- School of Mathematics - Associate Professor
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title = "Counting curves in hyperbolic surfaces",

abstract = "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.",

author = "Viveka Erlandsson and Juan Souto",

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doi = "10.1007/s00039-016-0374-7",

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journal = "Geometric and Functional Analysis",

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T1 - Counting curves in hyperbolic surfaces

AU - Erlandsson, Viveka

AU - Souto, Juan

PY - 2016/7/18

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N2 - 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.

AB - 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.

U2 - 10.1007/s00039-016-0374-7

DO - 10.1007/s00039-016-0374-7

M3 - Article (Academic Journal)

SN - 1016-443X

VL - 26

SP - 729

EP - 777

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

ER -

Counting curves in hyperbolic surfaces

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