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

  title={Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory},
  author={Gabriel P. Paternain and Leonid Polterovich and Karl Friedrich Siburg},
  journal={Moscow Mathematical Journal},
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 establish a new boundary rigidity phenomenon, saying that certain Lagrangians on the hypersurface cannot be deformed (via Lagrangians having the same Liouville class) into the interior domain. Moreover, we study the "non-removable intersection set" between the Lagrangian and the hypersurface, and show that it contains… Expand

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