A simpler proof of Mirzakhani's simple curve asymptotics
Geometric Topology
2007-05-23 v1 Dynamical Systems
Abstract
Maryam Mirzakhani (in her doctoral dissertation) has proved the author's conjecture that the number of simple curves of length bounded by L on a hyperbolic surface S is assymptotic to a constant times L to the power d, where d is the dimension of the Teichmuller space of S. In this note we clarify and simplify Mirzakhani's argument.
Cite
@article{arxiv.math/0512066,
title = {A simpler proof of Mirzakhani's simple curve asymptotics},
author = {Igor Rivin},
journal= {arXiv preprint arXiv:math/0512066},
year = {2007}
}
Comments
preliminary version of a paper published in Geometriae Dedicata