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

Omar Alehyane¹ ; Hichame Amal²

¹ Département de Mathématiques Faculté des Sciences Université Chouaib Doukkali B.P. 20, El Jadida, Maroc
² Département de Mathématiques Faculté des Sciences Université Mohammed V B.P 1014, Rabat, Maroc

Annales Polonici Mathematici, Tome 81 (2003) no. 3, pp. 201-215

Résumé

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 ${\mathbb D}^*$-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.

Détail

DOI : 10.4064/ap81-3-1

Mots-clés : paper study relationship between hyperbolicity complex spaces extension holomorphic mappings hartogs theorem separately holomorphic mappings prove complex space weak hyperbolicity which has mathbb * extension property has hartogs extension property consequence generalization picard theorem finally generalize teradas theorem separately holomorphic mappings