Finiteness of the Hofer-Zehnder capacity of neighborhoods of symplectic submanifolds
Finiteness of the Hofer-Zehnder capacity of neighborhoods of symplectic submanifolds
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DOI：
10.1155/imrn/2006/76520
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发表时间：
2005-10
影响因子：
1
通讯作者：
Guangcun Lu
中科院分区：
文献类型：
--
作者：
Guangcun Lu
我们利用Sternberg和Weinstein的最小耦合过程和我们的伪辛容量理论证明了任何辛流形中的每个闭辛子流形都有一个具有有限($pi_1敏感)Hofer-Zehnder辛容量的开邻域。因此，在任何辛流形中，Weinstein猜想都在闭辛子流形附近成立。
We use the minimal coupling procedure of Sternberg and Weinstein and our pseudo-symplectic capacity theory to prove that every closed symplectic submanifold in any symplectic manifold has an open neighborhood with finite ($\pi_1$-sensitive) Hofer-Zehnder symplectic capacity. Consequently, the Weinstein conjecture holds near closed symplectic submanifolds in any symplectic manifold.