Simple Curves on Surfaces

@article{Rivin1999SimpleCO,
  title={Simple Curves on Surfaces},
  author={Igor Rivin},
  journal={Geometriae Dedicata},
  year={1999},
  volume={87},
  pages={345-360}
}
  • Igor Rivin
  • Published 7 July 1999
  • Mathematics, Physics
  • Geometriae Dedicata
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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