A note on complex Monge-Ampère equation in Stein manifolds
type: Item
instance of: scholarly article
title: A note on complex Monge-Ampère equation in Stein manifolds
zbMATH Open document ID: 1155.32028
author: Alireza Bahraini
published in: The Asian Journal of Mathematics
publication date: 2008-08-18T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ajm/1213798134
review text: This paper studies the complex Monge-Ampère equation in Stein manifolds with boundary. More precisely, the author shows that given a compact \(n\)-dimensional Stein manifold with boundary \(X\), a \((1,1)\)-Kähler form \(\omega\) on \(X\), a function \(f\in C^\infty(X)\), and a function \(\phi\in C^\infty(\partial X)\), there exists a unique smooth function \(u\in C^\infty(X)\) such that \(\omega+i\partial\overline{\partial}u>0\) solving the complex Monge-Ampère equation \((\omega+i\partial\overline{\partial}u)^n=e^f\omega^n\) and satisfying the boundary condition \(u| _{\partial X}=\phi\).
reviewed by: Marco Abate
Mathematics Subject Classification ID: 32W20
Mathematics Subject Classification ID: 58J32
zbMATH DE Number: 5312750
zbMATH Keywords: Monge-Ampère equation
zbMATH Keywords: Stein manifolds with boundary
MaRDI profile type: Publication
OpenAlex ID: W2036554449
DOI: 10.4310/AJM.2008.V12.N1.A6
description: scientific article; zbMATH DE number 5312750