Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory

Gabriel P. Paternain, Leonid Polterovich, Karl Friedrich Siburg

We consider Lagrangian submanifolds lying on a fiberwise strictly convex hypersurface in some cotangent bundle or, respectively, in the domain bounded by such a hypersurface. We es…