Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields.
New invariants and their application to the equivalence problem
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 compact boundaries of complex analytic varieties in Hilbert spaces
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H.We deal with the problem by cutting with a family of complex hyperplanes and applying the already known result for the compact case.
Non completely solvable systems of complex first order PDEs
Non embeddable CR-structures
Nondegeneracy conditions and normal forms for real hypersurfaces in complex space
Non-embeddable CR-manifolds and surface singularities.
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
Note on pull-back and Lelong number of currents