On the Compactness of Hamiltonian Stationary Lagrangian Surfaces in K{\"a}hler Surfaces

We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian Stationary Lagrangian surfaces with bounded areas and Willmore energies in a complete K{"a}hler surface. We also prove two strong compactness theorems on the space of Hamiltonian stationary Lagrangian tori in $\mathbb C^2$and$$\mathbb{C}\mathbb{P}$^2$ respectively.