Geometrical and analytical properties of Chebyshev sets in Riemannian manifolds

de Lima, Ronaldo

doi:10.1090/proc/12793

Geometrical and analytical properties of Chebyshev sets in Riemannian manifolds
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by Ronaldo Freire de Lima PDF

Proc. Amer. Math. Soc. 144 (2016), 1697-1710 Request permission

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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