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

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.

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closed geodesics, hyperbolic surfaces
Mathematical Subject Classification
Primary: 32G15
Secondary: 30F10, 30F45, 53C22
Received: 31 August 2020
Revised: 25 April 2022
Accepted: 13 May 2022
Published: 1 August 2022
Hanh Vo
Department of Mathematics
University of Luxembourg