摘要翻译：
研究了Fano流形上沿Kahler Ricci流的一些估计。利用这些估计，我们直接证明了当标准类的$\alpha$-不变量大于$\frac{n}{n+1}$时，Kahler Ricci流的收敛性。应用这些收敛性定理，我们可以给出这类Fano流形上的Calabi猜想的流证明。特别是用流方法证明了许多Fano曲面上Kahler Einstein度量的存在性。注意，这个几何结论（基于同样的假设）是由G.Tian在较早的时候通过椭圆法建立的。然而，一个基于Kahler Ricci流的新证明本身应该仍然很有趣。
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英文标题：
《Remarks on Kahler Ricci Flow》
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作者：
Xiuxiong Chen, Bing Wang
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Differential Geometry        微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  We study some estimates along the Kahler Ricci flow on Fano manifolds. Using these estimates, we show the convergence of Kahler Ricci flow directly if the $\alpha$-invariant of the canonical class is greater than $\frac{n}{n+1}$. Applying these convergence theorems, we can give a flow proof of Calabi conjecture on such Fano manifolds. In particular, the existence of Kahler Einstein metrics on a lot of Fano surfaces can be proved by flow method. Note that this geometric conclusion (based on the same assumption) was established earlier via elliptic method by G. Tian. However, a new proof based on Kahler Ricci flow should be still interesting in its own right.
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PDF链接：
https://arxiv.org/pdf/0809.3963