We extend two celebrated theorems on closed geodesics of Riemannian 2-spheres to the larger class of reversible Finsler 2-spheres: Lusternik–Schnirelmann’s theorem asserting the existence of three simple closed geodesics, and Bangert–Franks–Hingston’s theorem asserting the existence of infinitely many closed geodesics. To prove the first theorem, we employ the generalization of Grayson’s curve shortening flow developed by Angenent–Oaks.
Closed geodesics on reversible Finsler 2-spheres
De Philippis G.;
2022
Abstract
We extend two celebrated theorems on closed geodesics of Riemannian 2-spheres to the larger class of reversible Finsler 2-spheres: Lusternik–Schnirelmann’s theorem asserting the existence of three simple closed geodesics, and Bangert–Franks–Hingston’s theorem asserting the existence of infinitely many closed geodesics. To prove the first theorem, we employ the generalization of Grayson’s curve shortening flow developed by Angenent–Oaks.
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