Effective counting of simple closed geodesics on hyperbolic surfaces
Geometric Topology
2021-07-06 v2 Dynamical Systems
Abstract
We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most 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.
Cite
@article{arxiv.1905.04435,
title = {Effective counting of simple closed geodesics on hyperbolic surfaces},
author = {Alex Eskin and Maryam Mirzakhani and Amir Mohammadi},
journal= {arXiv preprint arXiv:1905.04435},
year = {2021}
}
Comments
50 pages