Hamiltonian non-displaceability conjecture for compact minimal Lagrangian submanifolds

Let $L$ be a compact connected minimal Lagrangian submanifold of an irreducible Hermitian symmetric space of compact type. Hamiltonian non-displaceability conjecture. The submanifold $L$ is Hamiltonian non-displaceable. This conjecture would extend the non-displaceability results established in the paper for Gauss images of certain isoparametric hypersurfaces to all compact connected minimal Lagrangian submanifolds in irreducible Hermitian symmetric spaces of compact type. The statement is presented as a conjecture based on the present work and private communication with Hajime Ono; its general case remains open.