报告人：Keita Kunikawa (Tohoku University)
题目：Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow
摘要: In this talk, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kahler- Einstein manifolds to more general Kahler manifolds including Fano manifolds by using the methodology proposed by T. Behrndt. We first consider a weighted measure on a Lagrangian manifold in such a Kahler manifold and investigate the variational problem of the Lagrangian for the weighted volume under Hamiltonian deformations. We call a stationary point and a local minimizer of the weighted volume f-minimal and Hamiltonian f-stable. We show such examples naturally appear in toric Fano manifolds. Moreover, we consider the generalized Lagrangian mean curvature flow which is introduced by Behrndt and also by Smoczyk-Wang. We generalize the result by H. Li, and show that if the initial Lagrangian is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable Lagrangian, then the generalized MCF converges to an f-minimal one. This is a joint work with Toru Kajigaya.