论文标题
非本地距离函数和几何规律性
Non-local distance functions and geometric regularity
论文作者
论文摘要
我们建立了集合的规律性（重新可相关性）与平滑非本地距离函数梯度振荡的合适估计之间的等价性。盖伊·戴维（Guy David），约瑟夫·费内鲁尔（Joseph Feneuil）和第三作者引入了这种距离的原型例子，作为较大的PDE理论的一部分。结果适用于所有维度和共同维度，不需要基本的拓扑假设，并且提供了令人惊讶的重新可及性分析特征。
We establish the equivalence between the regularity (rectifiability) of sets and suitable estimates on the oscillation of the gradient for smooth non-local distance functions. A prototypical example of such a distance was introduced, as part of a larger PDE theory, by Guy David, Joseph Feneuil, and the third author. The results apply to all dimensions and co-dimensions, require no underlying topological assumptions, and provide a surprisingly rich class of analytic characterizations of rectifiability.
