Nonsimple closed geodesics with given intersection number on hyperbolic surfaces

Wujie Shen

Nonsimple closed geodesics with given intersection number on hyperbolic surfaces

Geometric Topology 2025-08-05 v2

Authors: Wujie Shen

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.

Keywords

hyperbolic surfaces geodesics and riemannian geometry

Cite

@article{arxiv.2305.00638,
  title  = {Nonsimple closed geodesics with given intersection number on hyperbolic surfaces},
  author = {Wujie Shen},
  journal= {arXiv preprint arXiv:2305.00638},
  year   = {2025}
}

Comments

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

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