Bohr–Sommerfeld Lagrangian submanifolds as minima of convex functions
Bohr–Sommerfeld Lagrangian submanifolds as minima of convex functions
复制标题
作为凸函数最小值的玻尔-索末菲拉格朗日子流形
DOI：
10.4310/jsg.2020.v18.n1.a9
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发表时间：
2018
影响因子：
0.7
通讯作者：
Alexandre Vérine
中科院分区：
文献类型：
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作者：
Alexandre Vérine
本文证明了辛/K\“ahler流形X的闭Bohr-Sommerfeld Lagrange子流形Q对于定义在辛/复超平面截面Y的补空间中的某个”凸“耗尽函数都可以实现为Morse-Bott极小值.在K\“ahler的情况下，”凸“意味着严格的多重次调和，而在辛的情况下，它指的是一个刘维伪梯度的存在。特别地，$Q\subset X\setminus Y$是Eliashberg-Ganatra-Lazarev意义下的正则拉格朗日子流形。
We prove that every closed Bohr-Sommerfeld Lagrangian submanifold $Q$ of a symplectic/K\"ahler manifold $X$ can be realised as a Morse-Bott minimum for some 'convex' exhausting function defined in the complement of a symplectic/complex hyperplane section $Y$. In the K\"ahler case, 'convex' means strictly plurisubharmonic while, in the symplectic case, it refers to the existence of a Liouville pseudogradient. In particular, $Q\subset X\setminus Y$ is a regular Lagrangian submanifold in the sense of Eliashberg-Ganatra-Lazarev.