Filling Radius and Short Closed Geodesics of the $2$-Sphere

Sabourau, Stéphane

Bulletin de la Société Mathématique de France, Tome 132 (2004) no. 1, pp. 105-136.

Nous montrons que la longueur de la plus courte courbe non triviale parmi les géodésiques simples fermées d'indice zéro ou un et les géodésiques en huit d'indice nul fournit une minoration sur l'aire et le diamètre des deux-sphères riemanniennes.

We show that the length of the shortest nontrivial curve among the simple closed geodesics of index zero or one and the figure-eight geodesics of null index provides a lower bound on the area and the diameter of the Riemannian $2$-spheres.

Classification : 53C20
Keywords: filling radius, closed geodesics, $1$-cycles
Mot clés : rayon de remplissage, géodésiques fermées, un-cycles

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