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On some rigidity properties of mappings between CR-submanifolds in complex space

Francine Meylan;  Nordine Mir;  Dimitri Zaitsev — 2003

Journées équations aux dérivées partielles

We survey some recent results on holomorphic or formal mappings sending real submanifolds in complex space into each other. More specifically, the approximation and convergence properties of formal CR-mappings between real-analytic CR-submanifolds will be discussed, as well as the corresponding questions in the category of real-algebraic CR-submanifolds.

Lie group structures on groups of diffeomorphisms and applications to CR manifolds

M. Salah Baouendi;  Linda Preiss Rothschild;  Jörg Winkelmann;  Dimitri Zaitsev — 2004

Annales de l’institut Fourier

We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.

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