The length of a shortest geodesic loop

Abstract

We give a lower bound for the length of a non-trivial geodesic loop on a simply-connected and compact manifold of even dimension with a non-reversible Finsler metric of positive flag curvature. Harris and Paternain use this estimate in their recent paper to give a geometric characterization of dynamically convex Finsler metrics on the 2-sphere. To cite this article: H.-B. Rademacher, C. R. Acad. Sci. Paris, Ser. I 346 (2008).