Partial regularity for homogeneous complex Monge-Ampère equations
type: Item
instance of: scholarly article
title: Partial regularity for homogeneous complex Monge-Ampère equations
zbMATH Open document ID: 1152.32304
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2005-04-07T00:00:00Z
review text: In this note the authors briefly discuss how to prove the existence of almost smooth solutions of the following Dirichlet problem for the homogeneous complex Monge-Ampère equation: \[ (\pi^*_2\omega+ \partial\overline\partial \varphi)^{n+1}= 0\quad\text{on }\Sigma\times M,\tag{1} \] \[ \varphi|_{\partial\Sigma\times M}= \psi,\tag{2} \] where \(\Sigma\) is the unit disc in \(\mathbb C\). The authors present a new partial regularity theory for (1)--(2), which is obtained by studying foliations by holomorphic disks and their relation to (1)--(2). This note is a sequel to the authors' former paper [C. R., Math., Acad. Sci. Paris 340, No. 4, 287--290 (2005; Zbl 1069.32017)]. The results, announced in this paper and the cited one, will appear with details in the authors' preprint `Geometry of Kähler metrics and foliations by holomorphic discs' (2004), see arXiv:math/0507148.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 32W20
Mathematics Subject Classification ID: 35N15
zbMATH DE Number: 2153798
zbMATH Keywords: Monge-Ampère equation
zbMATH Keywords: partial regularity
zbMATH Keywords: almost smooth solution
author: X.-X. Chen
author: Gang Tian
MaRDI profile type: Publication
full work available at URL: j.crma.2004.11.024
OpenAlex ID: W2040581059
cites work: The space of Kähler metrics. II.
cites work: The space of Kähler metrics.
cites work: Uniqueness of extremal Kähler metrics
cites work: Holomorphic discs and the complex Monge-Ampère equation.
cites work: Q4852951
cites work: Complex Monge-Ampere and Symplectic Manifolds
DOI: 10.1016/J.CRMA.2004.11.024
description: scientific article; zbMATH DE number 2153798