Compactness of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds

TL;DR

This paper proves a compactness theorem for Hamiltonian stationary Lagrangian submanifolds in compact symplectic manifolds, under bounds on area and extrinsic curvature, advancing understanding of their geometric behavior.

Contribution

It establishes a new compactness result for Hamiltonian stationary Lagrangian submanifolds with uniform geometric bounds.

Findings

Proves a compactness theorem for Hamiltonian stationary Lagrangian submanifolds.

Shows that bounds on area and extrinsic curvature ensure compactness.

Enhances understanding of the geometric structure of these submanifolds.

Abstract

In this work, we prove a compactness theorem on the space of all Hamiltonian stationay Lagrangian submanifolds in a compact symplectic manifold with uniform bounds on area and total extrinsic curvature.