| Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory Elektronische Daten (2003) | |||||||||||
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| Boundary rigidity for Lagrangian submanifolds non removable intersections and Aubry Mather theory Gabriel Paternain Department Pure Mathematics and Mathematical Statistics University Cambridge Cambridge England Leonid Polterovich School Mathematical Sciences Tel Aviv University Tel Aviv Israel Karl Friedrich Siburg Fakult Mathematik Ruhr Universit Bochum Bochum Germany March Supported Supported the United States Israel Binational Science Foundation grant Heisenberg grant the Deutsche Forschungsgemeinschaft Contents Introduction and results Preliminaries and basic notations Boundary rigidity The convex case The nonconvex case Non removable intersections The nonconvex case The convex case Symplectic shapes open fiberwise convex domains Graph selectors Lagrangian submanifolds and boundary rigidity Generating functions quadratic infinity The graph selector proof Theorem Proof Theorem Brief summary Aubry Mather theory critical value Weak KAM solutions and Peierls barrier The Aubry set Minimizing optical hypersurfaces Non removable intersections the convex case Constructing Lagrangian sections proof Theorem Boundary rigidity general symplectic manifolds Introduction and results the present note continue theme which goes back Arnold seminal survey First steps symplectic topology Arn hypersurface cotangent bundle called optical bounds fiberwise strictly convex domain Likewise Lagrangian submanifold called optical lies optical hypersurface particularly important class examples given i | |||||||||||
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