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Geometrical and analytical properties of Chebyshev sets in Riemannian manifolds


Author: Ronaldo Freire de Lima
Journal: Proc. Amer. Math. Soc. 144 (2016), 1697-1710
MSC (2010): Primary 53B21; Secondary 58C25
DOI: https://doi.org/10.1090/proc/12793
Published electronically: August 12, 2015
MathSciNet review: 3451245
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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.


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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
Email: ronaldo@ccet.ufrn.br

DOI: https://doi.org/10.1090/proc/12793
Keywords: Chebyshev set, convex set, distance function, subharmonic
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
Article copyright: © Copyright 2015 American Mathematical Society

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