作为凸函数极小值的玻尔-索默菲尔德拉格朗日子流形

IF 0.6 3区 数学 Q3 MATHEMATICS
Alexandre Vérine
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引用次数: 4

摘要

证明了辛/K\ ahler流形$X$的每一个闭玻尔-索默菲尔德拉格朗日子流形$Q$对于定义在辛/复超平面截面$Y$补上的某个“凸”耗尽函数都可以被实现为Morse-Bott极小值。在K\ ahler情况下,“凸”指的是严格的多次调和,而在辛情况下,它指的是Liouville伪梯度的存在。特别地,Q\子集X\set - Y$是Eliashberg-Ganatra-Lazarev意义上的正则拉格朗日子流形。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bohr–Sommerfeld Lagrangian submanifolds as minima of convex functions
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.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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