Curve shortening and the topology of closed geodesics on surfaces

• 成果类型: Article
• 署名作者: Angenent, SB
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.162.1187
• 发表日期: 2005
• 页码: 1187-1241
• 关键词: evolution-equations; parabolic equation; plane-curves; rotation

摘要

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.