In this Note we state some results obtained studying the evolution of compact subsets of by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.
We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant sets...
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.
In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds of , in particular Levi flat ones. As a general scheme, we suppose that is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.
Si calcola esplicitamente con l'aiuto di un computer l'espressione di ogni germe di biolomorfismo in un punto di una iperquadrica reale in , che porti in . Tale germe risulta ovviamente una trasformazione lineare fratta, che lascia invariante.