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arXiv · 2207.02557

Periodic geodesics in singular spaces

Panos Papasoglu·Eric Swenson
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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($\kappa $) condition for some fixed $\kappa >0$ and $\pi_n(X)\ne 0$ for some $n>0$ then $X$ has a periodic geodesic. This condition is satisfied for example by locally CAT($\kappa $) manifolds. Our result applies more generally to compact locally uniquely geodesic spaces.

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Panos Papasoglu, Eric Swenson. 2022-07-06. Periodic geodesics in singular spaces. https://arxiv.org/abs/2207.02557

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