Local q-completeness of complements of smooth CR-submanifolds.
Localization of biholomorphisms for real hyperquadrics in : a computational approach
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.
Mappings of quadric Cauchy-Riemann manifolds.
New examples of non-locally embeddable structures (with no non-constant distributions)
We construct examples of non-locally embeddable structures. These examples may show some improvement on previous examples by Nirenberg, and Jacobowitz and Trèves. They are based on a simple construction which consists in gluing two embedded structures. And (this is our main point) we believe that these examples are very transparent, therefore easy to work with.
Non embeddable CR-structures
Nondegeneracy conditions and normal forms for real hypersurfaces in complex space
Non-Realizable CR Structures.
Non-solvability of the tangential -systems
We prove that for a real analytic generic submanifold of whose Levi-form has constant rank, the tangential -system is non-solvable in degrees equal to the numbers of positive and negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.
Note on double reflection and algebraicity of holomorphic mappings
On a construction of the normal Cartan connections for CR-structures
On boundary Hilbert differential complexes
On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle
In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every -smooth CR diffeomorphism between two globally minimal real analytic hypersurfaces in () is real analytic at every point...
On local geometry of finite multitype hypersurfaces
This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in . We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.
On some rigidity properties of mappings between CR-submanifolds in complex space
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.
On Strict Levi q-Convexity and q-Concavity on Domains with Piecewise Smooth Boundaries.
On the convergence of normalizations of real analytic surfaces near hyperbolic complex tangents.
On the Curvature of CR-Structures and its Covariant Derivatives.
On the extension of C.R. functions.
On the extension of holomorphic functions across a real hypersurface.
On the hull of holomorphy of an -manifold in