Riemannian manifolds are KKM spaces

Year 2019, , 64 - 73, 30.06.2019

Sehie Park

https://doi.org/10.31197/atnaa.513857

Cited By: 2

Abstract

Let (M,g) be a complete, finite-dimensional Riemannian manifold. Based on the fact that any geodesic convex subset of M is a KKM space, we establish the KKM theory on such subsets originated from the Knaster-Kuratowski-Mazurkiewitz theorem in 1929.

Keywords

Riemannian manifold, KKM theorem, Abstract convex space, Geodesic convex set

References

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