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

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dc.creatorPaternain, Gabriel P.
dc.creatorPolterovich, Leonid
dc.creatorSiburg, Karl Friedrich
dc.date2002-07-17
dc.date2003-02-14
dc.date.accessioned2026-07-07T04:49:42Z
dc.date.available2026-07-07T04:49:42Z
dc.descriptionWe 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 a set with specific dynamical behavior, known as Aubry set in Aubry-Mather theory.
dc.descriptionThe main new point of this revised and substantially enlarged version, with G.P. Paternain as new co-author, is the relation between non-removable intersections and Aubry-Mather theory
dc.identifierhttps://arxiv.org/abs/math/0207140
dc.identifierhttp://arxiv.org/abs/math/0207140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64526
dc.subjectSymplectic Geometry
dc.subjectDynamical Systems
dc.titleBoundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory
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