Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$
Differential Geometry
2026-05-28 v5 Metric Geometry
Abstract
Length-bounded sweepouts provide a method for bounding the length of the shortest closed geodesic of a closed manifold. In this paper, we generalize this approach to the case of compact 2-dimensional orbifolds homeomorphic to S^2 as well as compact 2-dimensional orbifolds with finite orbifold fundamental groups. We establish an inequality for the length of the shortest closed orbifold geodesic in terms of the diameter.
Cite
@article{arxiv.2406.02781,
title = {Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$},
author = {Jinxuan Chen},
journal= {arXiv preprint arXiv:2406.02781},
year = {2026}
}