Existence of coupled K\"ahler-Einstein metrics using the continuity method
Existence of coupled K\"ahler-Einstein metrics using the continuity method
复制标题
使用连续性方法耦合 K"ahler-Einstein 度量的存在性
DOI：
10.1142/s0129167x18500416
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Vamsi Pingali
中科院分区：
文献类型：
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作者：
Vamsi Pingali
本文证明了正则丛充足的复流形上耦合K\“ahler-Einstein度量的存在性。Hultgren和Nystr\“om利用变分法证明了这些度量的存在性。我们用连续性方法证明了这个结果。在证明估计的过程中，类似于通常的K\“ahler-Einstein度量，我们将Fano情况下的存在性简化为C^0估计。
In this paper we prove the existence of coupled K\"ahler-Einstein metrics on complex manifolds whose canonical bundle is ample. These metrics were introduced and their existence in the said case was proven by Hultgren and Nystr\"om using calculus of variations. We prove the result using the method of continuity. In the process of proving estimates, akin to the usual K\"ahler-Einstein metrics, we reduce existence in the Fano case to a C^0 estimate.