论文标题
RICCI流及其在RICCI流动的局部奇异性分析具有有限标量曲率
A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature
论文作者
论文摘要
我们通过在本地研究曲率爆破率来为RICCI流进行精致的奇异性分析。我们首先介绍了I型和II型单数点的一般定义，并表明这些确实是唯一可能的单数点类型。特别是，在任何单数点附近，Riemannian曲率张量必须至少以I型速率炸毁，这是Enders，Topping和第一作者的概括，并依赖于全球I型假设。我们还证明了RICCI张量的结果，以及Sesum结果的局部版本，即Ricci曲率必须在Ricci流的每个单数点附近爆炸，至少在I型速率上再次爆发。最后，我们展示了该理论对有界标态曲率流动的一些应用。
We develop a refined singularity analysis for the Ricci flow by investigating curvature blow-up rates locally. We first introduce general definitions of Type I and Type II singular points and show that these are indeed the only possible types of singular points. In particular, near any singular point the Riemannian curvature tensor has to blow up at least at a Type I rate, generalising a result of Enders, Topping and the first author that relied on a global Type I assumption. We also prove analogous results for the Ricci tensor, as well as a localised version of Sesum's result, namely that the Ricci curvature must blow up near every singular point of a Ricci flow, again at least at a Type I rate. Finally, we show some applications of the theory to Ricci flows with bounded scalar curvature.
