Minimizing curves in prox-regular subsets of Riemannian manifolds

Mohamad R. Pouryayevali; Hajar Radmanesh

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arXiv · 2102.09477

Minimizing curves in prox-regular subsets of Riemannian manifolds

Mohamad R. Pouryayevali·Hajar Radmanesh

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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.

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BibTeX RIS

Mohamad R. Pouryayevali, Hajar Radmanesh. 2021-02-18. Minimizing curves in prox-regular subsets of Riemannian manifolds. https://arxiv.org/abs/2102.09477

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