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Curve Shortening and the Topology of Closed Geodesics on Surfaces

Sigurd B. Angenent
Annals of Mathematics
Second Series, Vol. 162, No. 3 (Nov., 2005), pp. 1187-1241
Published by: Annals of Mathematics
Stable URL: http://www.jstor.org/stable/20159941
Page Count: 55
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Curve Shortening and the Topology of Closed Geodesics on Surfaces
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Abstract

We study "flat knot types" of geodesics on compact surfaces M². 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 M². We conclude existence of closed geodesics with prescribed flat knot types, provided the associated Conley index is nontrivial.

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