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09 February 2025
 
  » arxiv » 1609.0217

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Short closed geodesics with self-intersections
Viveka Erlandsson ; Hugo Parlier ;
Date 1 Sep 2016
AbstractOur main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer $k$, we are interested in the set of all closed geodesics with at least $k$ (but possibly more) self-intersections. Among these, we consider those of minimal length and investigate their self-intersection numbers. We prove that their intersection numbers are upper bounded by a universal linear function in $k$ (which holds for any hyperbolic surface). Moreover, in the presence of cusps, we get bounds which imply that the self-intersection numbers behave asymptotically like $k$ for growing $k$.
Source arXiv, 1609.0217
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