Lengths of three simple periodic geodesics on a Riemannian $2$-sphere

Yevgeny Liokumovich, Alexander Nabutovsky, Regina Rotman

Let $M$ be a Riemannian $2$-sphere. A classical theorem of Lyusternik and Shnirelman asserts the existence of three distinct simple non-trivial periodic geodesics on $M$. In this p…