Geometry of biinvariant subsets of complex semisimple Lie groups
Homogeneous Cauchy-Riemann structures
Infinitesimal automorphisms and deformations of parabolic geometries
We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally...
Kernels of Martinelli-Bochner type on hypersurfaces.
Local regularity for the tangential Cauchy-Riemann complex.
Morera conditions along real planes and a characterization of CR functions on boundaries of domains in CN.
Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields.
Non completely solvable systems of complex first order PDEs
Note on pull-back and Lelong number of currents
Obstructions to generic embeddings
Let be a relatively closed subset of a Stein manifold. We prove that the -cohomology groups of Whitney forms on and of currents supported on are either zero or infinite dimensional. This yields obstructions of the existence of a generic embedding of a CR manifold into any open subset of any Stein manifold, namely by the nonvanishing but finite dimensionality of some intermediate -cohomology groups.
On holomorphic extension of functions on singular real hypersurfaces in .
On iterations of Green type integrals for matrix factorizations of the Laplace operator
Convergence of special Green integrals for matrix factorization of the Laplace operator in is proved. Explicit formulae for solutions of -equation in strictly pseudo-convex domains in are obtained.
On left invariant CR structures on
There is a well known one–parameter family of left invariant CR structures on . We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.
On the Burns-Epstein invariants of spherical CR 3-manifolds
In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.
On the Conformal and CR Automorphism Groups.
On the extension of C.R. functions.
On the Kuranishi family of deformations of complex structures over a tubular neighborhood of a strongly pseudo convex boundary with complex dimension 3.
On the regularity of CR structures for almost CR vector bundles.
Problème de Plateau complexe dans les variétés kählériennes
L’étude du « problème de Plateau complexe » (ou « problème du bord ») dans une variété complexe consiste à caractériser les sous-variétés réelles de qui sont le bord de sous-ensembles analytiques de . Notre principal résultat traite le cas où est une variété complexe connexe et est une variété kählérienne disque convexe. Comme conséquence, nous obtenons des résultats de Harvey-Lawson [19], Dolbeault-Henkin [12] et Dinh [10]. Nous obtenons aussi une généralisation des théorèmes de Hartogs-Levi...
Regularity of the tangential Cauchy-Riemann complex and applications