We will prove the existence of closed quasigeodesics in compact Alexandrov spaces which can be approximated by Riemannian manifolds in the Lipschitz sense. By applying it, we will prove that every convex hypersurface in Euclidean spaces has a closed quasigeodesic.
Iwao Kishimoto. "Existence of closed quasigeodesic in Alexandrov spaces of some types." Proc. Japan Acad. Ser. A Math. Sci. 78 (3) 30 - 32, March 2002. https://doi.org/10.3792/pjaa.78.30