Anwendungen des Satzes von Picard.
Applications holomorphes de domaines disqués non bornés.
We give several extensions to unbounded domains of the following classical theorem of H. Cartan: A biholomorphism between two bounded complete circular domains of Cn which fixes the origin is a linear map. In our paper, pseudo-convexity plays a main role. Some precise study is done for the case of dimension two and the case where one of the domains is Cn.
Applications polynômiales à jacobienne constante
Approximation by proper holomorphic maps into convex domains
Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition
Let be a complex Banach space. Recall that admits afinite-dimensional Schauder decompositionif there exists a sequence of finite-dimensional subspaces of such that every has a unique representation of the form with for every The finite-dimensional Schauder decomposition is said to beunconditionalif, for every the series which represents converges unconditionally, that is, converges for every permutation of the integers. For short, we say that admits an unconditional F.D.D.We...
Approximation of holomorphic maps by algebraic morphisms
Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.
Asymptotic behaviors of complex analytic dynamical systems.
Attracting divisors on projective algebraic varieties
We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor D on a projective algebraic variety X to be attracting for a holomorphic map f:X → X.
Attraction des disques analytiques et continuité Höldérienne d'applications holomorphes propres
Auflösung der Entartungen holomorpher Abbildungen zwischen zweidimensionalen Mannigfaltigkeiten.
Auto-applications holomorphes propies des domaines polynomiaux rigides de C2.
We show that proper holomorphic self maps of pseudoconvex rigid polynomial domains in C2 are automorphisms.
Automorphism groups of minimal real-analytic CR manifolds
We show that the local automorphism group of a minimal real-analytic CR manifold is a finite dimensional Lie group if (and only if) is holomorphically nondegenerate by constructing a jet parametrization.
Automorphismes analytiques des produits continus de domaines bornés
Automorphisms of certain Stein mainfolds.
Average Growth Estimates for Hyperplane Sections of Entire Analytic Sets.
Barth-Lefschetz theorems for singular spaces.
Bernstein and De Giorgi type problems: new results via a geometric approach
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
Big Picard theorems for holomorphic mappings into the complement of moving hypersurfaces in .
Biholomorphic domains with inequivalent boundaries.