DENSE EXISTENCE OF PERIODIC REEB ORBITS AND ECH SPECTRAL INVARIANTS
DENSE EXISTENCE OF PERIODIC REEB ORBITS AND ECH SPECTRAL INVARIANTS
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DOI：
10.3934/jmd.2015.9.357
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发表时间：
2015-01-01
影响因子：
1.1
通讯作者：
Irie, Kei
中科院分区：
文献类型：
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作者：
Irie, Kei
在本文中，我们证明：（1）对于具有C-无穷一般切触形式的闭切触三流形，周期Reeb轨道的并是稠密的;（2）对于具有C-无穷一般黎曼度量的闭曲面，闭测地线的并是稠密的.关键的观察是三维Reeb流的C-无穷闭引理，这是从嵌入接触同调（ECH）谱不变量恢复体积的事实。
In this paper, we prove: (1) for any closed contact three-manifold with a C-infinity-generic contact form, the union of periodic Reeb orbits is dense; (2) for any closed surface with a C-infinity-generic Riemannian metric, the union of closed geodesics is dense. The key observation is a C-infinity-closing lemma for three-dimensional Reeb flows, which follows from the fact that the embedded contact homology (ECH) spectral invariants recover the volume.