On Extension Properties of Pluricomplex Green Functions

À condition que ${\Omega }^0$ est une domaine bornée dans ${ℂ}^n$ et $ℰ$ soit compact sous-ensemble de ${\Omega }^0$ en maintenant que $\Omega :={\Omega }^0\setminus ℰ$ soit connexe, cet article va examiner les propriétés d’extension de la fonction de Green pluricomplexe de $\Omega$ en sous-domaines strictement plus larges $\tilde{\Omega }$ de $\Omega$ comme une fonction de Green pluricomplexe. Le problème sera examiné quand ${\Omega }^0$ soit une domaine Reinhardt complète bornée pseduconvexe dans ${ℂ}^n$ et une étude détaillée sur unité disque ${\Delta }^2\subset {ℂ}^2$ sera fournie.

Let ${\Omega }^0$ be a bounded domain in ${ℂ}^n$ and $ℰ$ be a compact subset of ${\Omega }^0$ such that $\Omega :={\Omega }^0\setminus ℰ$ is connected. This paper deals with the study of the extension properties of the pluricomplex Green function of $\Omega$ to strictly larger subdomains $\tilde{\Omega }$ of $\Omega$ as a pluricomplex Green function. The problem will be studied when ${\Omega }^0$ is a pseudoconvex, bounded complete Reinhardt domain in ${ℂ}^n$ and a detailed study in unit bidisc ${\Delta }^2\subset {ℂ}^2$ will be provided.

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