Abstract:

In the first part of this talk, we consider the linear f-stability of f-minimal Lagrangian submanifolds. I will introduce a generalized version of Chen and Oh’s second variational formula for minimal lagrangians in Kähler manifolds, and then use it to show that every Lagrangian translating soliton and expanding soliton is f-stable. Then we turn to focus on dynamic stability of f-stable Lagrangians under generalized Lagrangian mean curvature flow in the second part. Some recent progress in this direction and open problems will be discussed.