Théorème de Poincaré–Alexander pour les domaines modèles

Peyron, Marianne

Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 353-356.

Le théorème de Poincaré–Alexander stipule quʼune application holomorphe définie sur un ouvert de la boule unité de ${\mathbb{C}}^n$ peut, sous certaines conditions, être prolongée en un biholomorphisme de la boule unité. Dans le cadre presque complexe, la boule unité nʼest plus, à biholomorphisme près, le seul domaine strictement pseudoconvexe et homogène. Un domaine strictement pseudoconvexe et homogène est biholomorphe à un « domaine modèle ». Nous donnons dans cet article une généralisation du théorème de Poincaré–Alexander pour les domaines modèles.

The Poincaré–Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of ${\mathbb{C}}^n$ 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.

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