On the Compactness of Hamiltonian Stationary Lagrangian Surfaces in K{ä}hler Surfaces

Abstract

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{ä}hler surface. We also prove two strong compactness theorems on the space of Hamiltonian stationary Lagrangian tori in ${\mathbb{C}}^2$ and ${\mathbb{CP}}^2$ respectively.

23 pages, 4 figures

References in corpus (1)

• Compactification of the space of Hamiltonian stationary Lagrangian submanifolds with bounded total extrinsic curvature and volume