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Closed geodesics on reversible Finsler 2-spheres

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arxiv 2002.00415 v2 pith:JYJZMOZZ submitted 2020-02-02 math.DG math.DSmath.SG

Guido De Philippis , Michele Marini , Marco Mazzucchelli , Stefan Suhr This is my paper
classification math.DGmath.DSmath.SG
keywords closedgeodesicsspherestheoremassertingexistencefinslerreversible
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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.

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