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

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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
- v.erlandssonbristol.acuk
- 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",

year = "2016",

month = jul,

day = "18",

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

language = "English",

volume = "26",

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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

Y1 - 2016/7/18

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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