论文标题
$ c^0 $ - Legendrian Submanifolds的限制
$C^0$-limits of Legendrian Submanifolds
论文作者
论文摘要
劳登巴赫（Laudenbach）和西科拉夫（Sikorav）证明，只要没有拓扑障碍，封闭的六个非拉格朗日式非拉格朗日次数次数可以立即取代。他们从中推断出，只要极限是平稳的，$ c^0 $ - 限制了某些歧管的Lagrangian Submanifolds又是Lagrangian。 在本说明中，我们将劳登巴赫和西科拉夫的想法扩展到联系流动。我们相应地证明，只要没有拓扑阻塞，就可以立即将某些非legendrian接触歧管的非legendrian submanifolds移位而不会产生短的Reeb和弦。从此将遵循的是，在某些假设下，$ c^0 $ - 限制了一系列具有统一边界的Reeb Chords的Legendrian Submanifolds，但前提是Legendrian，前提是极限是平稳的。
Laudenbach and Sikorav proved that closed, half-dimensional non-Lagrangian submanifolds of symplectic manifolds are immediately displaceable as long as there is no topological obstruction. From this they deduced that the $C^0$-limit of a sequence of Lagrangian submanifolds of certain manifolds is again Lagrangian, provided that the limit is smooth. In this note we extend Laudenbach and Sikorav's ideas to contact manifolds. We prove correspondingly that certain non-Legendrian submanifolds of contact manifolds can be displaced immediately without creating short Reeb chords as long as there is no topological obstruction. From this it will follow that under certain assumptions the $C^0$-limit of a sequence of Legendrian submanifolds with uniformly bounded Reeb chords is again Legendrian, provided that the limit is smooth.
