完备Khler流形上Khler-Ricci流的局部Harnack估计

Local Harnack estimate for Khler-Ricci flow on complete Khler manifold

本文首先给出非正规化Khler-Ricci流下曲率的发展方程,然后得到了关于曲率的Harnack量在满足曲率局部条件下所产生的一个特殊项CNS.通过对CNS的估计,得到了完备Khler流形上关于Khler-Ricci流的局部Harnack不等式.最后,作为主要定理的应用,我们将结果推广到数量曲率的情形.

In this paper, we firstly give the evolving equation of the curvature under the unnormalized Kaihler-Ricci flow. Then we get the extra term CNS which is determined by the Harnack quantity satisfying the local condition of the curvature. By using the estimate of CNS, we obtain the local Harnack estimate of Kaihler-Ricci flow on the complete Kahler manifold. As a corollary, we get a sharp derivative estimate of scalar curvature.