In this paper, we systematically study the heat kernel of the Ricci flows induced by Ricci shrinkers. We develop several estimates which are much sharper than their counterparts in general closed Ricci flows. Many classical results, including the optimal Logarithmic Sobolev constant estimate, the Sobolev constant estimate, the no-local-collapsing theorem, the pseudo-locality theorem and the strong maximum principle for curvature tensors, are essentially improved for Ricci flows induced by Ricci shrinkers. Our results provide many necessary tools to analyze short time singularities of the Ricci flows of general dimension.

中文翻译：

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Ricci收缩机上的热核

在本文中，我们系统地研究了由Ricci收缩器引起的Ricci流的热核。我们得出了一些估计，这些估计要比一般的封闭Ricci流量中的估计要精确得多。对于Ricci收缩器引起的Ricci流动，许多经典结果，包括最佳对数Sobolev常数估计，Sobolev常数估计，无局部收缩定理，拟局部定理和曲率张量的强最大原理，都得到了根本改善。我们的结果提供了许多必要的工具来分析广义Ricci流的短时间奇点。