Each homotopically homogeneous tube in has an affine-homogeneous base.
Edge-of-the-wedge theorem for elliptic systems
Elementary pseudoconcavity and fields of CR meromorphic functions
Elimination of singularities on Hölder peak sets for functions
Embeddings of three dimensional Cauchy-Riemann manifolds.
Ensembles pics pour A°°(D) non globalement inclus dans une variété integrale.
Equivariant holomorphic extensions of real analytic manifolds
Estimates of the Kobayashi-Royden metric in almost complex manifolds
We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in and to give a sufficient condition for the complete hyperbolicity of a domain in .
Étude de la régularité analytique de l'application de réflexion CR formelle
Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere
We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.
Extension d'homéomorphismes CR entre variétés polynômialement rigides.
Let f : M → M' be a CR homeomorphism between two minimal, rigid polynomial varieties of Cn without holomorphic curves. We show that f extends biholomorphically in a neighborhood of M if f extends holomorphically in a neighborghood of a point p0 ∈ M or if f is of class C1. In the other hand, in case M and M' are two algebraic hypersurfaces, we obtain the extension without supplementary conditions.
Extension of -forms and related problems
Extension of CR functions to «wedge type» domains
Let be a complex manifold, a generic submanifold of , the real underlying manifold to . Let be an open subset of with analytic, a complexification of . We first recall the notion of -tuboid of and of and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for to the extendability of functions on to -tuboids of . Next, if has complex dimension 2, we give results on extension...
Extensions d'objets CR.