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19 April 2024

» arxiv » math.SG/0207140

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Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory
Gabriel P. Paternain ; Leonid Polterovich ; Karl Friedrich Siburg ;
Date:	17 Jul 2002
Subject:	Symplectic Geometry; Dynamical Systems \| math.SG math.DS
Abstract:	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 a set with specific dynamical behavior, known as Aubry set in Aubry-Mather theory.
Source:	arXiv, math.SG/0207140
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