Minimizing curves in prox-regular subsets of Riemannian manifolds
Differential Geometry
2021-02-19 v1
Abstract
We obtain a characterization of the proximal normal cone to a prox-regular subset of a Riemannian manifold. Moreover, some properties of Bouligand tangent cones to prox-regular sets are described. We prove that for a prox-regular subset S of a Riemannian manifold, the metric projection P_S to S is locally Lipschitz on an open neighborhood of S and it is directionally differentiable at boundary points of S. Finally, a necessary condition for a curve to be a minimizing curve in a prox-regular set is derived.
Keywords
Cite
@article{arxiv.2102.09477,
title = {Minimizing curves in prox-regular subsets of Riemannian manifolds},
author = {Mohamad R. Pouryayevali and Hajar Radmanesh},
journal= {arXiv preprint arXiv:2102.09477},
year = {2021}
}