The extendability of \(S\)-plurisubharmonic currents
type: Item
instance of: scholarly article
title: The extendability of \(S\)-plurisubharmonic currents
zbMATH Open document ID: 1262.32037
author: Ahmad K. Al Abdulaali
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2013-01-16T00:00:00Z
review text: The author proves the following result: If \(A\) is a closed pluripolar subset of an open subset \(\Omega\) of \(\mathbb C^{n}\) and \(T\) is a positive \(S\) plurisuperharmonic current of bidegree \((p,p)\) on \(\Omega\setminus A\) such that the \(2p-1\) Hausdorff measure \(\mathcal H_{2p-1}(A\cap\overline{\text{Supp T}})\) is zero, then one can extend this current through \(A\) to a current on the whole \(\Omega\) which moreover obeys the property that the extension of \(dd^{c} T\), less the \(dd^{c}\) of the extension, is positive and supported in \(A\). \(S\) plurisuperharmonicity means that the \(dd^c\) of this current is dominated by some positive current \(S\) of bidegree \((p+1,p+1)\) (note the misprint in the paper). The findings of this paper can be seen as a generalization of a classical result by Harvey.
Mathematics Subject Classification ID: 32U40
zbMATH DE Number: 6126004
zbMATH Keywords: \(S\)-plurisubharmonic currents
zbMATH Keywords: Hausdorff measure
reviewed by: Żywomir Dinew
MaRDI profile type: Publication
full work available at URL: j.crma.2012.10.032
OpenAlex ID: W1996337305
cites work: The inductive wedge product of positive currents
cites work: Wedge product of positive currents and balanced manifolds
cites work: Extension of plurisubharmonic currents
cites work: Pull-back of currents by holomorphic maps
cites work: Sur le prolongement des courants positifs fermés
cites work: Removable Singularities for Positive Currents
cites work: On the removal of singularities of analytic sets
DOI: 10.1016/J.CRMA.2012.10.032
description: scientific article; zbMATH DE number 6126004