Effective counting of simple closed geodesics on hyperbolic surfaces

Alex Eskin; Maryam Mirzakhani; Amir Mohammadi

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arXiv · 1905.04435

Effective counting of simple closed geodesics on hyperbolic surfaces

Alex Eskin·Maryam Mirzakhani·Amir Mohammadi

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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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BibTeX RIS

Alex Eskin, Maryam Mirzakhani, Amir Mohammadi. 2019-05-11. Effective counting of simple closed geodesics on hyperbolic surfaces. https://arxiv.org/abs/1905.04435

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