Curve shortening and the topology of closed geodesics on surfaces
Curve shortening and the topology of closed geodesics on surfaces
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DOI：
10.4007/annals.2005.162.1185
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发表时间：
2005-11
影响因子：
4.9
通讯作者：
S. Angenent
中科院分区：
文献类型：
--
作者：
S. Angenent
我们学习？平结型的紧曲面M2上的测地线。对于每一个平坦的纽结类型和任何黎曼度量g，我们引入了一个康利指数与曲线缩短流的浸入曲线的空间上的M2。我们得出结论，存在封闭测地线与规定的平结类型，提供相关的康利指数是非平凡的。
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.