In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for \(C^0\) metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from \(C^0\) initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from \(C^0\) initial data.

中文翻译：

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通过正则化Ricci流对$$ C ^ 0 $$ C0度量的逐点下标量曲率边界

在本文中，我们提出了一类弱的较低标量曲率边界的局部定义，该局部定义对于\（C ^ 0 \）度量定义良好。我们显示以下内容：我们的定义在度量的二阶以上扰动下是稳定的，存在一个合理的概念，即Ricci流从\（C ^ 0 \）初始数据开始，对于正数时间是平滑的，并且弱的下标量曲率界线在\（C ^ 0 \）初始数据的Ricci流作用下得以保留。