Existence of Lelong numbers of positive plurisuperharmonic currents
type: Item
instance of: scholarly article
title: Existence of Lelong numbers of positive plurisuperharmonic currents
zbMATH Open document ID: 1341.32030
author: Noureddine Ghiloufi
published in: Bulletin des Sciences Mathématiques
publication date: 2016-01-28T00:00:00Z
review text: The main result of this paper is the following: Let \(\Omega\) be an open subset of \(\mathbb C^n\) and \(T\) be a positive plurisuperharmonic \((i\partial\overline\partial T\leq 0)\) current of bidimension \((p,p)\) on \(\Omega\), where \(0<p<n\). Then, there exists a pluripolar subset \(E_T\) of \(\Omega\) such that the Lelong number \(\nu_T(z)\) exists for every \(z\in\Omega\smallsetminus E_T\). Moreover, if \(z\in\Omega\) such that \(\nu_T(z)\) exists then it does not depend on the system of coordinates. As an application, the author proves a result on the geometric structure of a positive plurisuperharmonic current and studies the existence of the current \(T=i\partial u\wedge\overline\partial u\) and its Lelong number, where \(u\) is a plurisubharmonic function.
reviewed by: Fredj Elkhadhra
Mathematics Subject Classification ID: 32U25
Mathematics Subject Classification ID: 32U40
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 6536790
zbMATH Keywords: Lelong numbers
zbMATH Keywords: plurisubharmonic functions
zbMATH Keywords: positive plurisuperharmonic currents
MaRDI profile type: Publication
full work available at URL: j.bulsci.2014.12.007
OpenAlex ID: W2079361256
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DOI: 10.1016/J.BULSCI.2014.12.007
description: scientific article; zbMATH DE number 6536790