Geometriae Dedicata

, Volume 87, Issue 1, pp 345–360

Simple Curves on Surfaces


  • Igor Rivin
    • Mathematics DepartmentUniversity of Manchester
    • Mathematics DepartmentTemple University

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.


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© Kluwer Academic Publishers 2001