Symmetries of partial differential equations

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations

Levi-flat filling of real two-spheres in symplectic manifolds (I)

Let (M,J,w) be a manifold with an almost complex structure J tamed by a symplectic form w. We suppose that M has complex dimension two, is Levi convex and has bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of M may be foliated by the boundaries of pseudoholomorphic discs.Comment: 18 page

Wong-Rosay Theorem in almost complex manifolds

We study the compactness of sequences of diffeomorphisms in almost complex manifolds in terms of the direct images of the standard integrable structure.Comment: date de redaction: 2003-6-1