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arXiv · 2406.02781

Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$

Jinxuan Chen
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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.

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Jinxuan Chen. 2024-06-04. Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$. https://arxiv.org/abs/2406.02781

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