A correction to ``The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function''
type: Item
instance of: scholarly article
title: A correction to ``The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function''
zbMATH Open document ID: 0949.32014
author: Bo Guan
published in: Communications in Analysis and Geometry
publication date: 2000-11-27T00:00:00Z
review text: The main result of the author's previous paper [ibid. 6, 687-703 (1998; Zbl 0923.31005)] is Theorem 1.2 which states that the pluricomplex Green function of a smooth, bounded, strongly pseudoconvex domain \(\Omega\subset \mathbb{C}^n\) with a logarithmic pole at \(\zeta\in\Omega\) belongs to \(C^{1,\alpha}(\overline\Omega\setminus \{\zeta\})\) for any \(\alpha\in (0,1)\). In the present note, the author indicates that the proof of that theorem is incomplete because it makes use of Lemma 3.1 whose proof contains an error. A new proof of Theorem 1.2 independent of Lemma 3.1 is presented.
Mathematics Subject Classification ID: 32U35
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32W20
zbMATH DE Number: 1423043
zbMATH Keywords: complex Monge-Ampère equation
zbMATH Keywords: pluricomplex Green function
MaRDI profile type: Publication
DOI: 10.4310/CAG.2000.V8.N1.E7
description: scientific article; zbMATH DE number 1423043