Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques

• Autorzy: O. Alehyane , A. Zeriahi
• Języki publikacji: FR EN

Abstrakty

EN

This paper is concerned with the problem of extension of separately holomorphic mappings defined on a "generalized cross" of a product of complex analytic spaces with values in a complex analytic space.
The crosses considered here are inscribed in Borel rectangles (of a product of two complex analytic spaces) which are not necessarily open but are non-pluripolar and can be quite small from the topological point of view.
Our first main result says that the singular set of a given separately holomorphic mapping defined on such a cross is quite small from the pluripotential point of view in the product space in the sense that each of its projections is pluripolar.
Then for some special crosses, we deduce more precise results on the extension of separately holomorphic mappings on such crosses, giving generalizations of all the main results obtained earlier by various authors in this direction.

Kategorie tematyczne

• 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
• 32D15: Continuation of analytic objects
• 31C10: Pluriharmonic and plurisubharmonic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2001
• Tom: 76
• Numer: 3
• Strony: 245-278

Daty

wydano

2001

Twórcy

autor

O. Alehyane

• Département de Mathématiques, Université Chouaib Doukkali, Faculté des Sciences, B.P. 20, El Jadida, Maroc

autor

A. Zeriahi

• Laboratoire de Mathématiques Emile Picard, UMR-CNRS 5580, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse, France

Identyfikatory

DOI

10.4064/ap76-3-5