Extension of correspondences between rigid polynomial domains
type: Item
instance of: scholarly article
title: Extension of correspondences between rigid polynomial domains
zbMATH Open document ID: 1109.32014
author: Nabil Ourimi
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2006-03-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73655
review text: The author studies the holomorphic extension of proper holomorphic correspondences between so called rigid polynomial domains, either in \(\mathbb{C}^{2}\), or, when the domains are also convex, in \(\mathbb{C}^{n}\). The set of holomorphic extendability of such a correspondence is shown to be a dense subset of the boundary. Moreover, it is the complement of the set of boundary points \(P\) where \(\overline{\lim}_{z \rightarrow P}| f(z)| = \infty\) (\(f\) is the correspondence). It is noteworthy that pseudoconvexity of the domains is not required. In a second theorem, the author shows that if the target domain is (in addition) stronly pseudoconvex, then any irreducible correspondence is a mapping.
Mathematics Subject Classification ID: 32H40
Mathematics Subject Classification ID: 32H35
zbMATH DE Number: 5010154
zbMATH Keywords: proper holomorphic correspondences
zbMATH Keywords: rigid polynomial domains
zbMATH Keywords: strongly pseudoconvex domains
reviewed by: Emil J. Straube
MaRDI profile type: Publication
OpenAlex ID: W2313823381
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DOI: 10.5802/AFST.1100
description: scientific article; zbMATH DE number 5010154