On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds

Dominic Joyce, Yng-Ing Lee, Richard Schoen

Let (M,w) be a compact symplectic 2n-manifold, and g a Riemannian metric on M compatible with w. For instance, g could be Kahler, with Kahler form w. Consider compact Lagrangian su…