Abstract: This talk consists of two parts related to the invariant submanifold of Kahler manifold. The first
part is about the variational characterizations of holomorphic submanifolds in Kahler manifold. This is based
on joint work with Claudio Arezzo at ICTP. We will also mention recent progress on variational
characterizations of invariant submanifold in Sasaki manifold. The second part is about two approaches to the
existence of holomorphic curves in Kahler surface. One is the symplectic mean curvature flow and the other is
the deformataion of symplectic critical surfaces. This is based on joint work with Xiaoli Han and Jiayu Li.