Nonsimple closed geodesics with given intersection number on hyperbolic surfaces

Abstract

We prove that the minimal length of a closed geodesic with self-intersection number $k$ on any finite-type hyperbolic surface is $2{\cosh }^{-1}(1+2k)$ for $k>1750$. This improves the previously known threshold $k>10^{13350}$. Our proof is independent of it.

21 pages, 7 figures. arXiv admin note: text overlap with arXiv:2207.08360