Sums of continuous plurisubharmonic functions and the complex Monge- Ampère operator in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Sums of continuous plurisubharmonic functions and the complex Monge- Ampère operator in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0624.31004
DOI: 10.1007/BF01229804
author: Urban Cegrell
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173792
review text: In pluricomplex analysis of n variables, the nonlinear complex Monge- Ampère equation \((dd^ c)^ n\) plays the same role as the Laplacian operator for one complex variable. Unfortunately, for V an arbitrary plurisubharmonic function, it is not always possible to define \((dd^ cV)^ n\). In their now classical work, \textit{E. Bedford} and \textit{B. A. Taylor} [Acta Math. 149, 1-40 (1982; Zbl 0547.32012)] showed that one can define \((dd^ cV)^ n\) for V locally bounded. The author shows that one can define \((dd^ cV)^ n\) for all \(V=\sum^{\infty}_{j=1}V_ j\) for \(V_ j\) continuous negative plurisubharmonic functions such that the sums \((dd^ c \sum^{N}_{j=1}V_ j)\) is uniformly bounded on complex subsets of D independently of N. He also studies convergence properties for the Monge-Ampère equation in this class of plurisubharmonic functions.
Mathematics Subject Classification ID: 31C10
zbMATH DE Number: 4013010
zbMATH Keywords: pluricomplex analysis
zbMATH Keywords: nonlinear complex Monge-Ampère equation
zbMATH Keywords: plurisubharmonic
zbMATH Keywords: convergence properties
reviewed by: Lawrence Gruman
MaRDI profile type: Publication
cites work: A new capacity for plurisubharmonic functions
cites work: Q3310999
cites work: Q3695586
cites work: Q3701749
cites work: Extension of meromorphic maps into Kähler manifolds
description: scientific article; zbMATH DE number 4013010