#### Vol. 318, No. 1, 2022

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Short closed geodesics on cusped hyperbolic surfaces

### Hanh Vo

Vol. 318 (2022), No. 1, 127–151
DOI: 10.2140/pjm.2022.318.127
##### Abstract

This article deals with the set of closed geodesics on complete finite type hyperbolic surfaces. For any nonnegative integer $k$, we consider the set of closed geodesics that self-intersect at least $k$ times and investigate those of minimal length. The main result is that, if the surface has at least one cusp, their self-intersection numbers are exactly $k$ for large enough $k$.

##### Keywords
closed geodesics, hyperbolic surfaces
##### Mathematical Subject Classification
Primary: 32G15
Secondary: 30F10, 30F45, 53C22
##### Milestones
Revised: 25 April 2022
Accepted: 13 May 2022
Published: 1 August 2022
##### Authors
 Hanh Vo Department of Mathematics University of Luxembourg Esch-sur-Alzette Luxembourg