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Local Minimality of Weak Geodesics on Prox-Regular Subsets of Riemannian Manifolds

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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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Funding

Juan Ferrera is partially supported by the Grant No: PID2022-138758NB-I00 (Spain) and Hajar Radmanesh is supported by the Iran National Science Foundation (INSF) under project No. 4002602.

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Authors and Affiliations

  1. IMI, Departamento de Análisis Matemático y Matemática Aplicada, Facultad Ciencias Matemáticas, Universidad Complutense, 28040, Madrid, Spain

    Juan Ferrera

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

    Mohamad R. Pouryayevali & Hajar Radmanesh

Authors
  1. Juan Ferrera
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  2. Mohamad R. Pouryayevali
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  3. Hajar Radmanesh
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The Contributions of three authors are equal.

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Correspondence to Mohamad R. Pouryayevali.

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Mohamad R. Pouryayevali declare he has no financial interests.

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Ferrera, J., Pouryayevali, M.R. & Radmanesh, H. Local Minimality of Weak Geodesics on Prox-Regular Subsets of Riemannian Manifolds. Mediterr. J. Math. 21, 110 (2024). https://doi.org/10.1007/s00009-024-02648-7

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  • DOI: https://doi.org/10.1007/s00009-024-02648-7

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