Geometriae Dedicata

, Volume 87, Issue 1, pp 345–360

Simple Curves on Surfaces

  • Igor Rivin

DOI: 10.1023/A:1012010721583

Cite this article as:
Rivin, I. Geometriae Dedicata (2001) 87: 345. doi:10.1023/A:1012010721583


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.


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.