Simple Curves on Surfaces

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 L 6g+2b+2c−6. This answers a long-standing open question.

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Rivin, I. Simple Curves on Surfaces. Geometriae Dedicata 87, 345–360 (2001). https://doi.org/10.1023/A:1012010721583

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  • hyperbolic
  • surface
  • geodesic
  • asymptotics