## Asian Journal of Mathematics

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

#### 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