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On subextension and approximation of plurisubharmonic functions with given boundary values

100%

Amal H.

Annales Polonici Mathematici

2014

tom 110

nr 3

247-258

Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in $𝓔_χ(Ω,H)$, the class of functions with finite χ-energy and given boundary values. We show that, under certain conditions, one can approximate any function in $𝓔_χ(Ω,H)$ by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

Propriétés d'extension et applications séparément holomorphes dans les espaces faiblement hyperboliques

63%

Alehyane O., Amal H.

Annales Polonici Mathematici

2003

tom 81

nr 3

201-215

The goal of this paper is to study the relationship between the hyperbolicity of complex spaces, extension of holomorphic mappings and the Hartogs theorem for separately holomorphic mappings. We prove that a complex space with a weak hyperbolicity which has the 𝔻*-extension property has the Hartogs extension property. As a consequence we give a generalization of the big Picard theorem. Finally we generalize Terada's theorem for separately holomorphic mappings.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Amal H.

1 Alehyane O.

1 2014

1 2003

Wyniki wyszukiwania

On subextension and approximation of plurisubharmonic functions with given boundary values

Propriétés d'extension et applications séparément holomorphes dans les espaces faiblement hyperboliques