Lagrangean Isotopy Problem and Special Lagrangian Submanifolds in Symplectic Geometry

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The seminar paper of M. Gromov on pseudoholomorphic curves had started a new era in the symplectic geometry. The theory developed there, as also the Donaldson and Seiber-Witten theories, are probably the most spectacular manifestation of the following principle of modern differential geometry: The study of properties of global solutions of certain non-linear elliptic PDEs related to the problem gives deep insight into the geometry of the underlying manifold. The aim of the proposed research project is to apply this principle to the theory of Lagrangean submanifolds in symplectic manifolds, in which the corresponding PDE is imposed by the special Lagrangean condition, and then use the developed techniques in the study of the Lagrangean isotopy problem.