1Département de Mathématiques Université Chouaib Doukkali Faculté des Sciences, B.P. 20 El Jadida, Maroc 2Laboratoire de Mathématiques Emile Picard UMR-CNRS 5580 Université Paul Sabatier 118 route de Narbonne F-31062 Toulouse, France
Annales Polonici Mathematici, Tome 76 (2001) no. 3, pp. 245-278
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.
Mots-clés :
paper concerned problem extension separately holomorphic mappings defined generalized cross product complex analytic spaces values complex analytic space crosses considered here inscribed borel rectangles product complex analytic spaces which necessarily non pluripolar quite small topological point view first main result says singular set given separately holomorphic mapping defined cross quite small pluripotential point view product space sense each its projections pluripolar special crosses deduce precise results extension separately holomorphic mappings crosses giving generalizations main results obtained earlier various authors direction
Affiliations des auteurs :
O. Alehyane
1
;
A. Zeriahi
2
1
Département de Mathématiques Université Chouaib Doukkali Faculté des Sciences, B.P. 20 El Jadida, Maroc
2
Laboratoire de Mathématiques Emile Picard UMR-CNRS 5580 Université Paul Sabatier 118 route de Narbonne F-31062 Toulouse, France
@article{10_4064_ap76_3_5,
author = {O. Alehyane and A. Zeriahi},
title = {Une nouvelle version du th\'eor\`eme d'extension
de {Hartogs} pour les applications s\'epar\'ement
holomorphes entre espaces analytiques},
journal = {Annales Polonici Mathematici},
pages = {245--278},
year = {2001},
volume = {76},
number = {3},
doi = {10.4064/ap76-3-5},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap76-3-5/}
}
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AU - O. Alehyane
AU - A. Zeriahi
TI - Une nouvelle version du théorème d'extension
de Hartogs pour les applications séparément
holomorphes entre espaces analytiques
JO - Annales Polonici Mathematici
PY - 2001
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EP - 278
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%A O. Alehyane
%A A. Zeriahi
%T Une nouvelle version du théorème d'extension
de Hartogs pour les applications séparément
holomorphes entre espaces analytiques
%J Annales Polonici Mathematici
%D 2001
%P 245-278
%V 76
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O. Alehyane; A. Zeriahi. Une nouvelle version du théorème d'extension
de Hartogs pour les applications séparément
holomorphes entre espaces analytiques. Annales Polonici Mathematici, Tome 76 (2001) no. 3, pp. 245-278. doi: 10.4064/ap76-3-5
