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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.

Keywords

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