Regular holomorphic images of balls
Every -dimensional complex manifold (connected, paracompact and Hausdorff) is the image of the unit ball in under a finite holomorphic map that is locally biholomorphic.
Regularity of the tangential Cauchy-Riemann complex and applications
Regularity of varieties in strictly pseudoconvex domains.
We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in Cn are also given.
Regularization of currents and entropy
Relative embeddings of discs into convex domains.
Remark on hyperbolic embeddability of relatively compact subspaces of complex spaces
Abstract. The characterization of hyperbolic embeddability of relatively compact subspaces of a complex space in terms of extension of holomorphic maps from the punctured disc and of limit complex lines is given.
Retractions régulières.
Reversible complex Hénon maps.
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 surfaces in Stein manifolds with the Density property
We show that any open Riemann surface can be properly immersed in any Stein manifold with the (Volume) Density property and of dimension at least 2. If the dimension is at least 3, we can actually choose this immersion to be an embedding. As an application, we show that Stein manifolds with the (Volume) Density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.
Riemann's existence problem for a p-adic field.
Rigidity of Holomorphic Self-Mappings and the Automorphism Groups of Hyperbolic Stein Spaces.
Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains
We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain . The generalized Fock-Bargmann-Hartogs domain is defined by inequality , where . In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain becomes a holomorphic automorphism if and only if it keeps the function invariant.
Schottky-Landau growth estimates for s-normal families of holomorphic mappings.
Schwarz Reflection Principle, Boundary Regularity and Compactness for -Complex Curves
We establish the Schwarz Reflection Principle for -complex discs attached to a real analytic -totally real submanifold of an almost complex manifold with real analytic . We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in -classes.
Second order differential subordinations of holomorphic mappings on bounded convex balanced domains in .
Self-dual magnetic monopoles and generalizations of holomorphic functions
Singularités des courants d'Ahlfors
Some compactness theorems of families of proper holomorphic correspondences.
In this paper we prove some compactness theorems of families of proper holomorphic correspondences. In particular we extend the well known Wong-Rosay's theorem to proper holomorphic correspondences. This work generalizes some recent results proved in [17].
Some criteria for the injectivity of holomorphic mappings
We prove some criteria for the injectivity of holomorphic mappings.