Shortest filling geodesics on hyperbolic surfaces
Yue Gao, Jiajun Wang, Zhongzi Wang · arXiv (Cornell University) · 2025
In this paper, we obtain the minimal length of a filling (multi-)geodesic on a genus $g$ 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 $(8g-4)$-gon. A single geodesic realizing this minimum is provided.