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