Résultats d'unicité de Cauchy instable dans des situations où la condition de pseudo-convexité dégénère
Riemann maps in almost complex manifolds
We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.
Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension 2.
Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
Let and be two compact strongly pseudoconvex CR manifolds of dimension which bound complex varieties and with only isolated normal singularities in and respectively. Let and be the singular sets of and respectively and is nonempty. If and the cardinality of is less than 2 times the cardinality of , then we prove that any non-constant CR morphism from to is necessarily a CR biholomorphism. On the other hand, let be a compact strongly pseudoconvex CR manifold of...
Rigidity of CR submanifolds and analyticity of CR immersions.
Singuläre Integrale mit gemsichten Homogenitäten auf Mannigfaltigkeiten und Anwendungen in der Funktionentheorie.
Smoothness of Cauchy Riemann maps for a class of real hypersurfaces.
We study the regularity problem for Cauchy Riemann maps between hypersurfaces in Cn. We prove that a continuous Cauchy Riemann map between two smooth C∞ pseudoconvex decoupled hypersurfaces of finite D'Angelo type is of class C∞.
Sobolev Estimates for the Lewy Operator on Weakly Pseudo-Convex Boundaries.
Solution operators for the ...-equation on non-transversal intersections.
Solutions de l’équation et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes
Il est montré que la condition de Blaschke est nécessaire et suffisante pour qu’un sous-ensemble analytique du domaine soit l’ensemble des zéros d’une fonction de la classe de Nevanlinna.
Solutions to -equations on strongly pseudo-convex domains with -estimates.
Some characterizations of Bloch functions on strongly pseudoconvex domains
Some properties of Reinhardt domains
We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk into D can be extended holomorphically to a map from Δ into D.
Special Toeplitz operators on strongly pseudoconvex domains.
Toeplitz operators on strongly pseudoconvex domains in Cn, constructed from the Bergman projection and with symbol equal to a positive power of the distance to the boundary, are considered. The mapping properties of these operators on Lp, as the power of the distance varies, are established.
Spherical Hypersurfaces in Complex Manifolds.
Stein Neighborhoods for Finite Preimages of Regular Domain.
Strictly pseudohyperbolic domains.
Subelliptic estimates
Sur la pseudo-convexité et la convexité polynomiale en dimension infinie
Dans la première partie, nous étudions la pseudo-convexité dans les elc et montrons que, dans le cas normé comme dans le cas non normé, les diverses notions introduites coïncident. Dans la deuxième partie, nous étudions la convexité polynomiale et prouvons des théorèmes d’approximation du type Runge ou Oka-Weil.
Sur la singularité des noyaux de Bergman et de Szegö