The Theorem of Lusternik&Schnirelmann for reversible Finsler metrics

The Theorem on the existence of three simple closed geodesics on every Riemannian 2-sphere has a “colorful” history and many applications on closed geodesics. I will give an introduction to the problem and outline a proof for the reversible Finsler case. Finally I will comment on some applications for closed geodesics. The talk is based on a collaboration with De Philippis, Marini, and Mazzucchelli.