Convergence of formal invertible CR mappings between minimal holomorphically nondegenerate real analytic hypersurfaces.
CR mappings between real hypersurfaces in complex space
CR singular immersions of complex projective spaces.
CR structures with group action and extendability of CR function.
CR submanifolds of maximal CR dimension in complex manifolds
The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.
Cylindrical real hyper surfaces in
Si stabiliscono due condizioni sufficienti per un germe di ipersuperficie reale di classe in affinchè esistano coordinate olomorfe rispetto alle quali l'ipersuperficie risulti essere il luogo di zeri di una funzione di variabili e sia minimale rispetto a questa proprietà. In altre parole si vuole che l'ipersuperficie, a meno di una trasformazione bi-olomorfa, sia l’unione di sottovarietà lineari complesse, parallele di dimensione .
Deformations of a complex mainfold near a strongly pseudo-convex real hypersurface and a realization of Kuranishi family of strongly pseudo-convex CR structures.
Deformations of Strictly Pseudoconvex Domains.
Each homotopically homogeneous tube in has an affine-homogeneous base.
Edge-of-the-wedge theorem for elliptic systems
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 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.
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.