2018/03/19 by Vérine, Alexandre
#53 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1803.07162
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⊂ X∖ Y is a regular Lagrangian submanifold in the sense of Eliashberg-Ganatra-Lazarev.