This paper is devoted to the study of the normal (tangential) regularity of a closed set and the subdifferential (directional) regularity of its distance function in the context of Riemannian manifolds. The Clarke, Fréchet and proximal subdifferentials of the distance function from a closed subset in a Riemannian manifold are represented by corresponding normal cones of the set.

中文翻译：

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关于黎曼流形中集的正则性

本文致力于研究闭集的法向（切向）正则性及其距离函数在黎曼流形背景下的次微分（方向）正则性。黎曼流形中一个封闭子集的距离函数的 Clarke、Fréchet 和近端子微分由该集合的相应法向锥表示。