A Revision on Geodesic Pseudo-Convex Combination and Knaster-Kuratowski-Mazurkiewicz Theorem on Hadamard Manifolds

摘要

In this paper, we point out that a recent characterization of geodesic convex hull on Hadamard manifolds is not rigorous and explain why the characterization does not hold like it in linear spaces. Therefore, a definition of geodesic pseudo-convex combination is proposed to show that the Knaster-Kuratowski-Mazurkiewicz theorem still holds under some mild conditions on Hadamard manifolds.