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 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 -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