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arXiv:0705.3012 [math.DG]AbstractReferencesReviewsResources

Curve shortening and the topology of closed geodesics on surfaces

Sigurd B. Angenent

Published 2007-05-21Version 1

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.

Comments: 55 pages, published version
Journal: Ann. of Math. (2) 162 (2005), no. 3, 1187--1241
Categories: math.DG
Subjects: 53C44, 53C22, 58E10
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