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

@article{Paternain2002BoundaryRF, 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}, year={2002}, volume={3}, pages={593-619} }

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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