Construction de disques analytiques et régularité de fonctions holomorphes au bord.
Precise regularity up to the boundary of proper holomorphic mappings
Proper holomorphic mappings between rigid polynomial domains in C.
We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in C. 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.
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.
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