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On Extension Properties of Pluricomplex Green Functions
S. Zeynep Özal Kurşungöz1
1 Sabanci University, 34956, Tuzla, Istanbul, Turkey
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 2, pp. 329-356.

Let Ω 0 be a bounded domain in ℂ n and ℰ be a compact subset of Ω 0 such that Ω:=Ω 0 ∖ℰ is connected. This paper deals with the study of the extension properties of the pluricomplex Green function of Ω to strictly larger subdomains Ω ˜ of Ω as a pluricomplex Green function. The problem will be studied when Ω 0 is a pseudoconvex, bounded complete Reinhardt domain in ℂ n and a detailed study in unit bidisc Δ 2 ⊂ℂ 2 will be provided.

À condition que Ω 0 est une domaine bornée dans ℂ n et ℰ soit compact sous-ensemble de Ω 0 en maintenant que Ω:=Ω 0 ∖ℰ soit connexe, cet article va examiner les propriétés d’extension de la fonction de Green pluricomplexe de Ω en sous-domaines strictement plus larges Ω ˜ de Ω comme une fonction de Green pluricomplexe. Le problème sera examiné quand Ω 0 soit une domaine Reinhardt complète bornée pseduconvexe dans ℂ n et une étude détaillée sur unité disque Δ 2 ⊂ℂ 2 sera fournie.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1601
Classification: 32U35
Keywords: pluricomplex Green functions, convex functions, Reinhardt domains

S. Zeynep Özal Kurşungöz 1

1 Sabanci University, 34956, Tuzla, Istanbul, Turkey
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {On {Extension} {Properties} of {Pluricomplex} {Green} {Functions}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {329--356},
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S. Zeynep Özal Kurşungöz. On Extension Properties of Pluricomplex Green Functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 2, pp. 329-356. doi : 10.5802/afst.1601. https://afst.centre-mersenne.org/articles/10.5802/afst.1601/

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