Minimizing curves in prox-regular subsets of Riemannian manifolds

2021/02/18 by Pouryayevali, Mohamad R., Radmanesh, Hajar
#49J52 #58C06 #58C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.09477

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.

Related

• Local minimality of weak geodesics on prox-regular subsets of Riemannian manifolds
• Weak geodesics on prox-regular subsets of Riemannian manifolds
• Rectifiable curves in proximally smooth sets
• Nonconvex weak sharp minima on Riemannian manifolds
• Sweeping process by prox-regular sets in Riemannian Hilbert manifolds