Convergence of Lagrangian mean curvature flow in K\"ahler-Einstein manifolds

Abstract

In this paper, we give some convergence results of Lagrangian mean curvature flow under some stability conditions in a general K\"ahler-Einstein manifold. In particular, we prove that the flow will converge if the initial data is some small perturbation of stable minimal Lagrangian submanifold in a K\"ahler-Einstein manifold.