Compactness of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds

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.