Geodesic
Curve shortening and the topology of closed geodesics on surfaces
Sigurd B. Angenent1
1 Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706
Annals of mathematics, Tome 162 (2005) no. 3, pp. 1187-1241.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We study “flat knot types” of geodesics on compact surfaces $M^2$. For every flat knot type and any Riemannian metric $g$ we introduce a Conley index associated with the curve shortening flow on the space of immersed curves on $M^{2}$. We conclude existence of closed geodesics with prescribed flat knot types, provided the associated Conley index is nontrivial.
DOI : 10.4007/annals.2005.162.1187

Sigurd B. Angenent 1

1 Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 
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Sigurd B. Angenent. Curve shortening and the topology of closed geodesics on surfaces. Annals of mathematics, Tome 162 (2005) no. 3, pp. 1187-1241. doi : 10.4007/annals.2005.162.1187. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.1187/

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