A notion of extremal analytic discs related to interpolation in the ball.
A precise result on the boundary regularity of biholomorphic mappings (Erratum).
Attraction des disques analytiques et continuité Höldérienne d'applications holomorphes propres
B-regularity of certain domains in ℂⁿ
We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.
Condition and Fefferman's mapping theorem.
Construction de disques analytiques et régularité de fonctions holomorphes au bord.
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 .
Extension of correspondences between rigid polynomial domains
Extension of holomorphic maps between real hypersurfaces of different dimension
In this paper we extend the results on analytic continuation of germs of holomorphic mappings from a real analytic hypersurface to a real algebraic hypersurface to the case when the target hypersurface is of higher dimension than the source. More precisely, we prove the following: Let be a connected smooth real analytic minimal hypersurface in , be a compact strictly pseudoconvex real algebraic hypersurface in , . Suppose that is a germ of a holomorphic map at a point in and is in...
Hölder continuity of proper holomorphic mappings
We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.
Mappings of quadric Cauchy-Riemann manifolds.
Precise regularity up to the boundary of proper holomorphic mappings
Proper holomorphic mappings between rigid polynomial domains in Cn+1.
We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in Cn+1. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.
Reflection principle in higher dimensions.
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.
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.
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.
Uniform boundary regularity of proper holomorphic maps