Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds

Details Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds

2009-09-24

arxiv.org/abs/0909.4496v2

Asian J. Math. 14 (2010), no.1, 19-40

Mathematics

Differential Geometry

26 pages. Revised version has rewritten introduction to reflect added references; corollaries improved

Scientific paper

We generalize Yau's estimates for the complex Monge-Ampere equation on compact manifolds in the case when the background metric is no longer Kahler. We prove $C^{\infty}$ a priori estimates for a solution of the complex Monge-Ampere 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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