Geometrical and analytical properties of Chebyshev sets in Riemannian manifolds
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Abstract:
We discuss Chebyshev sets of Riemannian manifolds. These are closed sets characterized by the existence of a well-defined distance-realizing projection onto them. The results we establish relate analytical properties of the distance function to these sets to their geometrical properties. They are extensions of some theorems on Chebyshev sets in Euclidean space to the context of Riemannian manifolds.References
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Additional Information
- Ronaldo Freire de Lima
- Affiliation: Departamento de Matemática, Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Lagoa Nova, CEP 59.072-970, Brasil
- MR Author ID: 688566
- Email: ronaldo@ccet.ufrn.br
- Received by editor(s): October 14, 2014
- Received by editor(s) in revised form: March 26, 2015
- Published electronically: August 12, 2015
- Communicated by: Lei Ni
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1697-1710
- MSC (2010): Primary 53B21; Secondary 58C25
- DOI: https://doi.org/10.1090/proc/12793
- MathSciNet review: 3451245