Equations of Monge-Ampère type on compact Hermitian manifolds.
type: Item
instance of: scholarly article
title: Equations of Monge-Ampère type on compact Hermitian manifolds.
zbMATH Open document ID: 0847.53045
author: Abdellah Hanani
published in: Journal of Functional Analysis
publication date: 1996-06-23T00:00:00Z
review text: Let \((X,g)\) be a compact Hermitian manifold. For \(\varphi \in C^2 (X) \), let \(M (\varphi) = \text{det} (\delta^\lambda_\mu + \nabla^\lambda_\mu \varphi)\). The author studies equations of the form \[ M (\varphi) = F(x, \nabla \varphi; \varphi), \] where \(F \in C^\infty\) \((TX \times \mathbb{R})\) is an everywhere strictly positive function with exponential growth in \(|\varphi |\) which is bounded by a power of the norm of the gradient of \(\varphi\). See also 1. \textit{S. T. Yau}, Commun. Pure Appl. Math. 31, 339-411 (1978; Zbl 0369.53059); 2. \textit{P. Delanoe}, J. Funct. Anal. 40, 358-386 (1981; Zbl 0466.58029); 3. \textit{T. Aubin}, Nonlinear analysis on manifolds. Monge-Ampère equations, Springer-Verlag (New York--Berlin 1982; Zbl 0512.53044); 4. \textit{W. Y. Ding} and \textit{G. Tian}, Invent. Math. 110, No. 2, 315-335 (1992; Zbl 0779.53044).
reviewed by: Maido Rahula
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32W20
zbMATH DE Number: 871729
zbMATH Keywords: Monge-Ampere equations
zbMATH Keywords: compact Hermitian manifold
MaRDI profile type: Publication
full work available at URL: jfan.1996.0040
OpenAlex ID: W2016339516
DOI: 10.1006/JFAN.1996.0040
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description: scientific article; zbMATH DE number 871729