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
Received: 31 August 2020
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