Compactness of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds

Abstract

In this work, we prove a compactness theorem on the space of all Hamiltonian stationary Lagrangian submanifolds in a compact symplectic manifold with uniform bounds on area and total extrinsic curvature. This generalizes the compactness theorems in Chen and Warren [J. Differential Geom. 126 (2024), pp. 65–97] and Chen and Ma [Var. Partial Differential Equations 60 (2021), Paper No. 75, 23].