On the compactness of Hamiltonian stationary Lagrangian submanifolds

Let \$(M,\omega)\$ be a symplectic manifold with a compatible metric. A Lagrangian submanifold in \$M\$ is called Hamiltonian stationary (HSL) if it is a critical point of the volume functional among Hamiltonian Variations. In this talk, we discuss two compactness theorems on the space of HSL submanifold with uniformly bounded area and total extrinsic curvature. This is a joint work with Jingyi Chen.