English

Shortest filling geodesics on hyperbolic surfaces

Geometric Topology 2025-06-17 v1

Abstract

In this paper, we obtain the minimal length of a filling (multi-)geodesic on a genus gg hyperbolic surface in the moduli space of hyperbolic surfaces and show that it is realized by the geodesic whose complement is a right-angled regular (8g4)(8g-4)-gon. A single geodesic realizing this minimum is provided.

Keywords

Cite

@article{arxiv.2506.12465,
  title  = {Shortest filling geodesics on hyperbolic surfaces},
  author = {Yue Gao and Jiajun Wang and Zhongzi Wang},
  journal= {arXiv preprint arXiv:2506.12465},
  year   = {2025}
}

Comments

18 pages, 13 figures

R2 v1 2026-07-01T03:17:41.482Z