Asian Journal of Mathematics
Volume 14 (2010)
Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds
Pages: 19 – 40
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.
Complex Monge-Ampère equation; Hermitian manifold; balanced manifold
2010 Mathematics Subject Classification
Primary 32W20. Secondary 32Q25, 53C55.