Pseudoconvexity of Riemann domains over a product of complex planes
type: Item
instance of: scholarly article
title: Pseudoconvexity of Riemann domains over a product of complex planes
zbMATH Open document ID: 0926.32014
author: K. Appert
published in: Taiwanese Journal of Mathematics
publication date: 1999-11-18T00:00:00Z
review text: The authors prove the following result: Let \((\Omega,\phi)\) be a schlicht Riemann domain over \({\mathbb C}^{\mathbb N}\). If \(\Omega\) is pseudoconvex then there exists an \(n\in\mathbb N\) and a pseudoconvex Riemann domain \((V,\phi| V)\) over \({\mathbb C}^n\) such that \(\Omega={\mathbb C}^{{\mathbb N}\setminus\{1,\dots,n\}}\times V\). For \((\Omega,\phi)\) an open subset of \({\mathbb C}^{\mathbb N}\) the result was proved by \textit{A. Hirschowitz} [Ann. Inst. Fourier 19, No. 1, 219-229 (1969; Zbl 0207.08203)].
Mathematics Subject Classification ID: 32F17
Mathematics Subject Classification ID: 46E50
zbMATH DE Number: 1234922
zbMATH Keywords: Riemann domain
zbMATH Keywords: pseudoconvex domain
zbMATH Keywords: pluripolar set
reviewed by: Nicolae Mihalache
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406974
OpenAlex ID: W4234495582
DOI: 10.11650/TWJM/1500406974
description: scientific article; zbMATH DE number 1234922