Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications
type: Item
instance of: scholarly article
zbMATH Open document ID: 1341.32027
author: Hai Mau Le
author: Nguyen Xuan Hong
published in: Annales Polonici Mathematici
publication date: 2014-08-14T00:00:00Z
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32U15
Mathematics Subject Classification ID: 32W20
zbMATH DE Number: 6330463
zbMATH Keywords: complex Monge-Ampère operator
zbMATH Keywords: plurisubharmonic functions
MaRDI profile type: Publication
full work available at URL: ap112-1-5
OpenAlex ID: W2334125791
cites work: Subextension of plurisubharmonic functions without increasing the total Monge–Ampère mass
cites work: Pluripolar sets and the subextension in Cegrell's classes
cites work: Convergence in capacity
cites work: A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications
DOI: 10.4064/AP112-1-5
title: Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications
review text: The authors generalise the results of \textit{U. Cegrell} and \textit{A. Zeriahi} [C. R., Math., Acad. Sci. Paris 336, No. 4, 305--308 (2003; Zbl 1025.31005)] and \textit{R. Czyż} and \textit{L. Hed} [Ann. Pol. Math. 94, No. 3, 275--281 (2008; Zbl 1161.32019)] by showing that subextension with boundary values of certain plurisubharmonic functions is always possible without changing the Monge-Ampère measures. As an application, they investigate the Dirichlet problem for a non-negative measure \(\mu \) in the Cegrell class \({\mathcal F}(\Omega , g)\) without the assumption that \(\mu \) vanishes on all pluripolar sets.
reviewed by: Oliver Jones
description: scientific article; zbMATH DE number 6330463