Local minimality of weak geodesics on prox-regular subsets of Riemannian manifolds

Juan Ferrera; Mohamad R. Pouryayevali; Hajar Radmanesh

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arXiv · 2311.13256

Local minimality of weak geodesics on prox-regular subsets of Riemannian manifolds

Juan Ferrera·Mohamad R. Pouryayevali·Hajar Radmanesh

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Abstract

In this paper we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally minimizing. Furthermore a notion of closed weak geodesics on prox-regular sets is introduced and a characterization of these curves as nonsmooth critical points of the energy functional is presented.

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BibTeX RIS

Juan Ferrera, Mohamad R. Pouryayevali, Hajar Radmanesh. 2023-11-22. Local minimality of weak geodesics on prox-regular subsets of Riemannian manifolds. https://arxiv.org/abs/2311.13256

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