Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to S²

2024/06/04 by Jinxuan Chen, Chen, Jinxuan
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2406.02781

openalex publication_date 2024/06/04 · openalex created_date 2024/06/08 · openalex updated_date 2026/07/28

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 S² 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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