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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-3-1,
author = {Omar Alehyane and Hichame Amal},
title = {Propri\'et\'es d'extension et applications s\'epar\'ement holomorphes dans les espaces faiblement hyperboliques},
journal = {Annales Polonici Mathematici},
volume = {81},
year = {2003},
pages = {201-215},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-3-1}
}
Omar Alehyane; Hichame Amal. Propriétés d'extension et applications séparément holomorphes dans les espaces faiblement hyperboliques. Annales Polonici Mathematici, Tome 81 (2003) pp. 201-215. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-3-1/