A simpler proof of Mirzakhani's simple curve asymptotics

Details A simpler proof of Mirzakhani's simple curve asymptotics A simpler proof of Mirzakhani's simple curve asymptotics

2005-12-02

arxiv.org/abs/math/0512066v1

Geometriae dedicata, Vol 114, number 1, August 2005

Mathematics

Geometric Topology

preliminary version of a paper published in Geometriae Dedicata

Scientific paper

10.1007/s10711-005-7153

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.

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