Effective counting of simple closed geodesics on hyperbolic surfaces

2019/05/11 by Eskin, Alex, Mirzakhani, Maryam, Mohammadi, Amir · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1905.04435

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 Teichmüller geodesic flow.

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