We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

中文翻译：

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关于具有两侧曲率界限的流形的备注

我们讨论关于具有两侧有界曲率的流形中距离函数的民间传说。主题包括规律性、积极影响的子集和切割轨迹。