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What do 'convexities' imply on Hadamard manifolds?

 

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Author: Kristály, Alexandru
Li, Chong
López Acedo, Genaro
Nicolae, Adriana
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2016-09
Published in: Journal of Optimization Theory and Applications, 170 (3), 1068-1074.
Document type: Article
Abstract: Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these conditions are mutually equivalent and they hold if and only if the Hadamard manifold is isometric to the Euclidean space. In this way, we show that some results in the literature obtained on Hadamard manifolds are actually nothing but their well known Euclidean counterparts.
Cite: Kristály, A., Li, C., López Acedo, G. y Nicolae, A. (2016). What do 'convexities' imply on Hadamard manifolds?. Journal of Optimization Theory and Applications, 170 (3), 1068-1074.
Size: 1.219Mb
Format: PDF

URI: http://hdl.handle.net/11441/45141

DOI: 10.1007/s10957-015-0780-2

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