2022/10/24 by Ara Basmajian, Basmajian, Ara, Hugo Parlier +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2210.12966
openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).