Kähler–Ricci flow, Kähler–Einstein metric, and K–stability
Kähler–Ricci flow, Kähler–Einstein metric, and K–stability
复制标题
DOI：
10.2140/gt.2018.22.3145
复制
发表时间：
2015-08
影响因子：
2
通讯作者：
Xiuxiong Chen;Song Sun;B. Wang
中科院分区：
文献类型：
--
作者：
Xiuxiong Chen;Song Sun;B. Wang
我们使用 Kahler-Ricci 流的最新紧致性结果证明了 K 稳定 Fano 流形上 Kahler-Einstein 度量的存在性。关键要素是对 Fano 流形上 Kahler-Ricci 流渐近行为的代数几何描述。这又基于一般的有限维讨论，该讨论本身很有趣，并且可能适用于其他问题。作为一种应用，我们将极化卡勒流形上卡拉比流的渐进性与假设几何边界的 K 稳定性联系起来。
We prove the existence of Kahler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kahler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kahler-Ricci flow on Fano manifolds. This is in turn based on a general finite dimensional discussion, which is interesting in its own and could potentially apply to other problems. As one application, we relate the asymptotics of the Calabi flow on a polarized Kahler manifold to K-stability assuming bounds on geometry.