Curve shortening and the topology of closed geodesics on surfaces

Sigurd B. Angenent

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arXiv · 0705.3012

Curve shortening and the topology of closed geodesics on surfaces

Sigurd B. Angenent

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Abstract

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.

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BibTeX RIS

Sigurd B. Angenent. 2007-05-21. Curve shortening and the topology of closed geodesics on surfaces. https://arxiv.org/abs/0705.3012

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