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arXiv · 1803.07162

Bohr-Sommerfeld Lagrangian submanifolds as minima of convex functions

Alexandre Vérine
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Abstract

We prove that every closed Bohr-Sommerfeld Lagrangian submanifold $Q$ of a symplectic/Kähler 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 Kähler 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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Alexandre Vérine. 2018-03-19. Bohr-Sommerfeld Lagrangian submanifolds as minima of convex functions. https://arxiv.org/abs/1803.07162

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