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On subextension and approximation of plurisubharmonic functions with given boundary values

Hichame Amal — 2014

Annales Polonici Mathematici

Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in 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 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

Omar Alehyane;  Hichame Amal — 2003

Annales Polonici Mathematici

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.

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