Minimizing Curves in Prox-regular Subsets of Riemannian Manifolds

被引：0
作者：
Mohamad R. Pouryayevali
Hajar Radmanesh
机构：
[1] University of Isfahan,Department of Pure Mathematics, Faculty of Mathematics and Statistics
来源：
Set-Valued and Variational Analysis | 2022年 / 30卷
关键词：
Prox-regular sets; -convex sets; Metric projection; Nonsmooth analysis; Riemannian manifolds; 58C20; 58E30; 49J52;
D O I：
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学科分类号：
摘要：
We obtain a characterization of the proximal normal cone to a prox-regular subset of a Riemannian manifold and some properties of Bouligand tangent cones to these sets are presented. Moreover, we show that on an open neighborhood of a prox-regular set, the metric projection is locally Lipschitz and it is directionally differentiable at the boundary points of the set. Finally, a necessary condition for a curve to be a minimizing curve in a prox-regular set is derived.
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页码：677 / 694
页数：17
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