Some curvature estimates of Kähler-Ricci flow
Some curvature estimates of Kähler-Ricci flow
复制标题
Kähler-Ricci 流的一些曲率估计
DOI：
10.1090/proc/14436
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发表时间：
2019
影响因子：
1
通讯作者：
Luen
中科院分区：
文献类型：
--
作者：
Man;Luen
本文首先给出了Kähler流形上Kähler-Ricci流的一些局部曲率估计，这些局部曲率估计的初始度量为非负的对分曲率。作为推论，我们证明了如果是满足某些条件的Kähler-Ricci流的完全解，且有非负的对分曲率，则也有非负的对分曲率.这推广了[Amer. J. Math. 140（2018），pp. 189-220]和[J. Differential Geom.45（1997），pp. 94-220]。利用局部曲率估计，我们证明了：对于Kähler-Ricci流的完全解，若有非负的对分曲率，若非坍缩，且对所有的解，则对某些解，的曲率实际上有界于.特别地，具有非负的对分曲率。这个结果与Simon和Topping在Kähler类别中的结果相似。引用
In this work, first we will obtain some local curvature estimates for Kähler-Ricci flow on Kähler manifolds with initial metrics of nonnegative bisectional curvature. As a corollary, we prove that ifis a complete solution of the Kähler Ricci flow which satisfiesfor some,andhas nonnegative bisectional curvature, thenalso has nonnegative bisectional curvature. This generalizes results in [Amer. J. Math. 140 (2018), pp. 189–220] and [J. Differential Geom. 45 (1997), pp. 94–220]. Using the local curvature estimate, we prove that for a complete solutionof the Kähler-Ricci flow withto have nonnegative bisectional curvature, to be noncollapsing, andfor all, then the curvature ofis in fact bounded byfor some. In particular,has nonnegative bisectional curvature for. This result is similar to a result by Simon and Topping in the Kähler category. References