A characterization of totally real generic submanifolds of strictly pseudoconvex boundaries in Cn admitting a local foliation by interpolation submanifolds.
A Construction of Normal Forms for Weakly Pseudoconvex CR Manifolds in ...2.
A global invariant for three dimensional CR-manifolds.
A local Martinelli-Bochner formula on hypersurfaces.
A microlocal version of Cartan-Grauert's theorem
Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in .
A Precise Result on the Boundary Regularity of Biholomorphic Mappings.
Analycity of CR Equivalences Between Some Real Hypersurfaces in ...n with Degenerate Levi Forms.
Analytic disks with boundaries in a maximal real submanifold of
Let be a two dimensional totally real submanifold of class in . A continuous map of the closed unit disk into that is holomorphic on the open disk and maps its boundary into is called an analytic disk with boundary in . Given an initial immersed analytic disk with boundary in , we describe the existence and behavior of analytic disks near with boundaries in small perturbations of in terms of the homology class of the closed curve in . We also prove a regularity theorem...
Approximation of biholomorphic mappings by automorphisms of Cn (Erratum).
Approximation of biholomorphic mappings by automorphisms of Cn.
Automorphism groups of minimal real-analytic CR manifolds
We show that the local automorphism group of a minimal real-analytic CR manifold is a finite dimensional Lie group if (and only if) is holomorphically nondegenerate by constructing a jet parametrization.
Biholomorphic domains with inequivalent boundaries.
Boundaries of Levi-flat hypersurfaces: special hyperbolic points
Let S ⊂ ℂⁿ, n ≥ 3, be a compact connected 2-codimensional submanifold having the following property: there exists a Levi-flat hypersurface whose boundary is S, possibly as a current. Our goal is to get examples of such S containing at least one special 1-hyperbolic point: a sphere with two horns, elementary models and their gluings. Some particular cases of S being a graph are also described.
Canvexité rationnelle des surfaces lagrangiennes.
Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains
For a strongly pseudoconvex domain defined by a real polynomial of degree , we prove that the Lie group can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle of , and that the sum of its Betti numbers is bounded by a certain constant depending only on and . In case is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Chaînes holomorphes de bord donné dans
Classification of CR invariant structures for compact Lie groups. (Classification des structures CR invariantes pour les groupes de Lie compacts.)
∂̅-cohomology and geometry of the boundary of pseudoconvex domains
In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained how Hartogs...
Complex-Tangential Sets and Boundary Values in Submanifolds of the Boundary.