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Minimizing Curves in Prox-regular Subsets of Riemannian Manifolds

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Abstract

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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Acknowledgements

The second-named author was supported by a grant from the University of Isfahan. The authors would like to thank the anonymous referees for their comments that helped to improve the quality of the paper.

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  1. Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Iran

    Mohamad R. Pouryayevali & Hajar Radmanesh

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  1. Mohamad R. Pouryayevali
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  2. Hajar Radmanesh
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Correspondence to Mohamad R. Pouryayevali.

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Pouryayevali, M.R., Radmanesh, H. Minimizing Curves in Prox-regular Subsets of Riemannian Manifolds. Set-Valued Var. Anal 30, 677–694 (2022). https://doi.org/10.1007/s11228-021-00614-z

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