Abstract
The complex Monge-Ampere equation has been the subject ofintensive studies in the past fifty years, since its significant applications in complex analysis, complex geometry and Kahler geometry. In this paper, we will introduce our recent work on the Liouville type theorem, $C^{1,~\\alpha}$ and $C^{2,~\\alpha~}$ estimates of the complex Monge-Ampere equation and its applications in Sasakian geometry. These works are joint with S. Dinew, P. F. Guan, C. Li, J. Y. Li and X. W. Zhang.
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