Théorème de Poincaré-Alexander pour les domaines modèles. Poincare-Alexander Theorem for model domains.

Marianne Peyron (1)

1 IF - Institut Fourier

The Poincaré-Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of $C^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly pseudoconvex homogeneous domain is biholomorphic to the unit ball. In an almost complex manifold, the unit ball is not the only strongly pseudoconvex homogeneous domain. A strongly pseudoconvex homogeneous domain is biholomorphic to a model domain. The aim of this paper is to extend this theorem to model domains.

Mots clés: model domains; automorphism; strongly pseudoconvex; almost complex manifold

Domaines: Variables complexes [math.CV]

Marianne Peyron. Théorème de Poincaré-Alexander pour les domaines modèles. Poincare-Alexander Theorem for model domains.. 2012. ⟨hal-00751257v2⟩