Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds
Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds
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DOI：
10.4310/ajm.2010.v14.n1.a3
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发表时间：
2009-09
影响因子：
0.6
通讯作者：
Valentino Tosatti;B. Weinkove
中科院分区：
文献类型：
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作者：
Valentino Tosatti;B. Weinkove
当背景度量不再是卡勒时，我们将丘对紧流形上的复杂 Monge-Ampere 方程的估计进行推广。当背景度量为 Hermitian（在复数维度中）或平衡（在更高维度中）时，我们证明了复数 Monge-Ampere 方程解的先验估计 $C^{\infty}$ ，给出了 Cherrier 定理的替代证明。我们将此与管力最近的结果联系起来。
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.