Periodic geodesics in singular spaces

2022/07/06 by Panos Papasoglu, Papasoglu, Panos, Eric Swenson +1
Mathematics · #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.2207.02557

openalex publication_date 2022/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the classical result of Lyusternik and Fet on the existence of closed geodesics to singular spaces. We show that if X is a compact geodesic metric space satisfying the CAT(κ) condition for some fixed κ>0 and π_n(X)≠ 0 for some n>0 then X has a periodic geodesic. This condition is satisfied for example by locally CAT(κ) manifolds. Our result applies more generally to compact locally uniquely geodesic spaces.

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