Th\'eor\`eme de Poincar\'e-Alexander pour les domaines mod\`eles. Poincare-Alexander Theorem for model domains

TL;DR

This paper extends the Poincaré-Alexander Theorem to model domains in complex and almost complex manifolds, showing that strongly pseudoconvex homogeneous domains are biholomorphic to these models.

Contribution

The paper generalizes the Poincaré-Alexander Theorem to include model domains in almost complex manifolds, broadening the class of domains known to be biholomorphic to strongly pseudoconvex homogeneous domains.

Findings

Strongly pseudoconvex homogeneous domains are biholomorphic to model domains.

Extension of the Poincaré-Alexander Theorem to almost complex manifolds.

Identification of conditions under which biholomorphisms extend to model domains.

Abstract

The Poincar\'e-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.