Property \((P)\) and Stein neighborhood bases on \(C^1\) domains
type: Item
instance of: scholarly article
title: Property \((P)\) and Stein neighborhood bases on \(C^1\) domains
zbMATH Open document ID: 1175.32017
author: Phillip S. Harrington
published in: Illinois Journal of Mathematics
publication date: 2009-06-22T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1242414125
review text: For a bounded pseudo-convex domain \(\Omega\) in \(\mathbb C^n\) \((n\geq2)\), whose boundary is of class \(C^k\) \((k\geq1)\), the property \((P)\) means that for every \(M>0\), there exists a smooth plurisubharmonic function \(\lambda\) on \(\overline{\Omega}\) such that \(0\leq \lambda\leq 1\) on \(\overline{\Omega}\) and \(i\partial \overline{\partial}\lambda\geq iM\partial \overline{\partial}|z|^2\) on \( \partial\Omega\). By using an equivalent form of the \((P)\) property, the author shows in this paper that if \(k=1\), then \(\overline \Omega\) has a Stein neighbourhood basis. Thus improving a previous result which Sibony had proved for \(k=3\).
reviewed by: Eugen Pascu
Mathematics Subject Classification ID: 32T35
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32E10
zbMATH DE Number: 5567367
zbMATH Keywords: bounded pseudo-convex domain
zbMATH Keywords: Stein neighbourhood
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5567367