A characterization of Zoll Riemannian metrics on the 2-sphere

Abstract

The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any Riemannian 2-sphere whose simple length spectrum consists of only one element L, any geodesic is simple closed with length L.

11 pages, 1 figure. Version 2: added more details on Grayson's curve shortening flow

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