Closed geodesics on reversible Finsler 2-spheres

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. In order to prove the first theorem, we employ the generalization of Grayson's curve shortening flow developed by Angenent-Oaks.

57 pages, 4 figures; final version: a few corrections to Theorem 1.2, to Sections 2.5-6, and to Section 5.4

References in corpus (1)

• Closed geodesics with local homology in maximal degree on non-compact manifolds

Cited by in corpus (3)

• Existence of Birkhoff sections for Kupka-Smale Reeb flows of closed contact 3-manifolds
• From curve shortening to flat link stability and Birkhoff sections of geodesic flows
• Surfaces of section for geodesic flows of closed surfaces