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

Abstract

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.