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Markov Type of Alexandrov Spaces of Non-Negative Curvature Shin-Ichi Ohta

Part of: Global differential geometry Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  21 December 2009

Shin-Ichi Ohta
Shin-Ichi Ohta
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan, E-mail: sohta@math.kyoto-u.ac.jp
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Abstract

We prove that Alexandrov spaces of non-negative curvature have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz continuous map from a subset of an Alexandrov space of non-negative curvature into a 2-uniformly convex Banach space can be extended to a Lipschitz continuous map on the entire space.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
Type
Research Article
Information
Mathematika , Volume 55 , Issue 1-2 , December 2009 , pp. 177 - 189
Copyright
Copyright © University College London 2009

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