Asian Journal of Mathematics

Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds

Valentino Tosatti and Ben Weinkove

Full-text: Open access

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.

Article information

Source
Asian J. Math., Volume 14, Number 1 (2010), 19-40.

Dates
First available in Project Euclid: 8 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1286547517

Mathematical Reviews number (MathSciNet)
MR2726593

Zentralblatt MATH identifier
1208.32034

Subjects
Primary: 32W20: Complex Monge-Ampère operators
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 32Q25: Calabi-Yau theory [See also 14J30]

Keywords
Complex Monge-Ampère equation Hermitian manifold balanced manifold

Citation

Tosatti, Valentino; Weinkove, Ben. Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds. Asian J. Math. 14 (2010), no. 1, 19--40. https://projecteuclid.org/euclid.ajm/1286547517


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