In this paper, we obtain local derivative estimates of Shi-type for the heat equation coupled to the Ricci flow. As applications, in part combining with Kuang’s work, we extend some results of Zhang and Bamler–Zhang including distance distortion estimates and a backward pseudolocality theorem for Ricci flow on compact manifolds to the noncompact case.

中文翻译：

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耦合到 Ricci 流的热方程的局部导数估计

在本文中，我们获得了耦合到 Ricci 流的热方程的 Shi 型的局部导数估计。作为应用，部分结合 Kuang 的工作，我们将 Zhang 和 Bamler-Zhang 的一些结果包括距离失真估计和紧致流形上 Ricci 流的反向伪定域定理扩展到非紧致情况。