Estimates for the complex monge-ampère equation on hermitian and balanced manifolds

Valentino Tosatti; Ben Weinkove

doi:10.4310/AJM.2010.v14.n1.a3

Estimates for the complex monge-ampère equation on hermitian and balanced manifolds

Valentino Tosatti^*, Ben Weinkove

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

We generalize Yau's estimates for the complex Monge-Ampère equation on compact manifolds in the case when the background metric is no longer Kähler. We prove C^∞ a priori estimates for a solution of the complex Monge-Ampère equation when the background metric is Hermitian (in complex dimension two) or balanced (in higher dimensions), giving an alternative proof of a theorem of Cherrier. We relate this to recent results of Guan-Li.

Original language	English (US)
Pages (from-to)	19-40
Number of pages	22
Journal	Asian Journal of Mathematics
Volume	14
Issue number	1
DOIs	https://doi.org/10.4310/AJM.2010.v14.n1.a3
State	Published - Mar 2010

Keywords

Balanced manifold
Complex Monge-Ampère equation
Hermitian manifold

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4310/AJM.2010.v14.n1.a3

Cite this

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AB - We generalize Yau's estimates for the complex Monge-Ampère equation on compact manifolds in the case when the background metric is no longer Kähler. We prove C∞ a priori estimates for a solution of the complex Monge-Ampère equation when the background metric is Hermitian (in complex dimension two) or balanced (in higher dimensions), giving an alternative proof of a theorem of Cherrier. We relate this to recent results of Guan-Li.

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KW - Complex Monge-Ampère equation

KW - Hermitian manifold

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Estimates for the complex monge-ampère equation on hermitian and balanced manifolds

Abstract

Keywords

ASJC Scopus subject areas

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