Geometriae Dedicata

, Volume 87, Issue 1–3, pp 345–360 | Cite as

Simple Curves on Surfaces

  • Igor Rivin
Article

Abstract

We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order L6g+2b+2c−6. This answers a long-standing open question.

hyperbolic surface geodesic asymptotics 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Igor Rivin
    • 1
    • 2
  1. 1.Mathematics DepartmentUniversity of ManchesterManchesterU.K.
  2. 2.Mathematics DepartmentTemple UniversityPhiladelphiaU.S.A.

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