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

Li-wen Zhou () and Nan-jing Huang ()
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Li-wen Zhou: Southwest Petroleum University
Nan-jing Huang: Sichuan University

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 17, 1186-1198

Abstract: 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.

Keywords: Hadamard manifold; Geodesic convex hull; Geodesic pseudo-convex combination; KKM theorem; 49J40; 47J20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01511-0

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