Duality and distribution cohomology of manifolds
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.
Fibrés normaux d'immersions en dimension double, points doubles d'immersions lagrangiennes et plongements totalement réels.
Fields of CR meromorphic functions
Foliations with complex leaves
Fonctions et feuilletages Levi-Flat. Étude locale
We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.
Formule d'homotopie pour un domaine à bord (q+k)-concave d'une variété CR générique et q-concave. Applications
We give a homotopy formula for the operator on a domain with (q+k)-concave boundary. As a consequence we show that the dimension of the -cohomology groups for some CR manifolds q-concave at infinity is finite.