Differential Geometry
The length of a shortest geodesic loop
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 763-765.

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.

On donne une borne inférieure pour la longueur d'un lacet géodésique non-triviale sur une variété compacte et simplement connexe munie d'une métrique de Finsler non-reversible de courbure positive. Harris et Paternain utilisent cette éstimée dans leur récent article afin de donner und charactérisation géométrique des métriques de Finsler à convexité dynamique sur la sphère de dimension 2.

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DOI: 10.1016/j.crma.2008.06.001
Rademacher, Hans-Bert 1

1 Universität Leipzig, Mathematisches Institut, 04081 Leipzig, Germany
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Rademacher, Hans-Bert. The length of a shortest geodesic loop. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 763-765. doi : 10.1016/j.crma.2008.06.001. http://www.numdam.org/articles/10.1016/j.crma.2008.06.001/

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[7] Rademacher, H.B. Existence of closed geodesics on positively curved Finsler manifolds, Ergod. Theory Dynam. Systems, Volume 27 (2007), pp. 957-969

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