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Effective counting of simple closed geodesics on hyperbolic surfaces

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arxiv 1905.04435 v2 pith:BDHJWVBN submitted 2019-05-11 math.GT math.DS

Alex Eskin , Maryam Mirzakhani , Amir Mohammadi This is my paper · ORCID
classification math.GTmath.DS
keywords closedgeodesicssimplecompactcountingcurvatureeffectiveequipped
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abstract

We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichm\"{u}ller geodesic flow.

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  1. Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves

    math.GT 2019-08 conditional novelty 7.0 of 10

    Masur-Veech volumes of Qg,n are expressed as explicit polynomials in psi-class intersection numbers, and flat square-tiled counts are shown to match hyperbolic multicurve frequencies up to a normalization constant.

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