The shortest non-simple closed geodesics on hyperbolic surfaces
arXiv:2210.12966
Abstract
This article explores closed geodesics on hyperbolic surfaces. We show that, for sufficiently large , the shortest closed geodesics with at least self-intersections, taken among all hyperbolic surfaces, all lie on an ideal pair of pants and have length $2\arccosh(2k+1)$.
21 pages, 6 figures