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 -spheres.
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.
Keywords: filling radius, closed geodesics, $1$-cycles
Mot clés : rayon de remplissage, géodésiques fermées, un-cycles
@article{BSMF_2004__132_1_105_0, author = {Sabourau, St\'ephane}, title = {Filling {Radius} and {Short} {Closed} {Geodesics} of the $2${-Sphere}}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {105--136}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {132}, number = {1}, year = {2004}, doi = {10.24033/bsmf.2461}, mrnumber = {2075918}, zbl = {1064.53020}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/bsmf.2461/} }
TY - JOUR AU - Sabourau, Stéphane TI - Filling Radius and Short Closed Geodesics of the $2$-Sphere JO - Bulletin de la Société Mathématique de France PY - 2004 SP - 105 EP - 136 VL - 132 IS - 1 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/bsmf.2461/ DO - 10.24033/bsmf.2461 LA - en ID - BSMF_2004__132_1_105_0 ER -
%0 Journal Article %A Sabourau, Stéphane %T Filling Radius and Short Closed Geodesics of the $2$-Sphere %J Bulletin de la Société Mathématique de France %D 2004 %P 105-136 %V 132 %N 1 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/bsmf.2461/ %R 10.24033/bsmf.2461 %G en %F BSMF_2004__132_1_105_0
Sabourau, Stéphane. Filling Radius and Short Closed Geodesics of the $2$-Sphere. Bulletin de la Société Mathématique de France, Volume 132 (2004) no. 1, pp. 105-136. doi : 10.24033/bsmf.2461. http://archive.numdam.org/articles/10.24033/bsmf.2461/
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