On the local solution of the tangential Cauchy-Riemann equations
On the Nature of Thin Complements of Complete Kähler Metrics.
On the partial algebraicity of holomorphic mappings between two real algebraic sets
The rigidity properties of the local invariants of real algebraic Cauchy-Riemann structures imposes upon holomorphic mappings some global rational properties (Poincaré 1907) or more generally algebraic ones (Webster 1977). Our principal goal will be to unify the classical or recent results in the subject, building on a study of the transcendence degree, to discuss also the usual assumption of minimality in the sense of Tumanov, in arbitrary dimension, without rank assumption and for holomorphic...
On the Polynomial Convexity of the Union ot Two Maximal Totally Real Subspaces of Cn.
On the proof of Kuranishi's embedding theorem
On the real analytic Levi flat hypersurfaces in complex tori of dimension two
We compute the Levi form of the logarithm of the distance function for real hypersurfaces in two dimensional complex tori, and discuss the characterization of Levi flat hypersurfaces there.
On the smoothness of Levi-foliations.
We study the regularity of the induced foliation of a Levi-flat hypersurface in Cn, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.
On the space of the analytic discs which are transversal to a smooth real hypersurface of
On totally real submanifolds in a nearly Kähler manifold.
Partial indices of analytic discs attached to lagrangian submanifolds of
Integers are the partial indices of an analytic disc attached to a maximally real submanifolds of if and only if for at least one . If this is the case there are a Lagrangian submanifold of and an analytic disc attached to with partial indices .
Peak Sets in Weakly Pseudoconvex Domains.
Poincaré automorphisms for nondegenerate CR quadrics.
Poincaré Lemma for Tangential Cauchy Riemann Complexes.
Polydisc slicing in
Let D be the unit disc in the complex plane ℂ. Then for every complex linear subspace H in of codimension 1, . The lower bound is attained if and only if H is orthogonal to the versor of the jth coordinate axis for some j = 1,...,n; the upper bound is attained if and only if H is orthogonal to a vector for some 1 ≤ j < k ≤ n and some σ ∈ ℂ with |σ| = 1. We identify with ; by we denote the usual k-dimensional volume in . The result is a complex counterpart of Ball’s [B1] result for...
Polynomially Convex Hulls with Piecewise Smooth Boundaries.
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...
Projective Connections in CR Geometry.
Prolongement holomorphe d'applications CR
Prolongement unilatéral des fonctions CR
Proper Holomorphic Mappings Between Real-Analytic Pseudoconvex Domains in Cn.