The shortest non-simple closed geodesics on hyperbolic surfaces

Ara Basmajian; Hugo Parlier; Hanh Vo

The shortest non-simple closed geodesics on hyperbolic surfaces

Geometric Topology 2022-11-16 v2 Differential Geometry

Authors: Ara Basmajian , Hugo Parlier , Hanh Vo

Abstract

This article explores closed geodesics on hyperbolic surfaces. We show that, for sufficiently large $k$ , the shortest closed geodesics with at least $k$ self-intersections, taken among all hyperbolic surfaces, all lie on an ideal pair of pants and have length $2\arccosh(2k+1)$ .

Keywords

hyperbolic surfaces geodesics and riemannian geometry

Cite

@article{arxiv.2210.12966,
  title  = {The shortest non-simple closed geodesics on hyperbolic surfaces},
  author = {Ara Basmajian and Hugo Parlier and Hanh Vo},
  journal= {arXiv preprint arXiv:2210.12966},
  year   = {2022}
}

Comments

21 pages, 6 figures

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