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Kirszbraun's theorem and metric spaces of bounded curvature


Lang, U; Schroeder, V (1997). Kirszbraun's theorem and metric spaces of bounded curvature. Geometric and Functional Analysis, 7(3):535-560.

Abstract

We generalize Kirszbraun's extension theorem for Lipschitz maps between (subsets of) euclidean spaces to metric spaces with upper or lower curvature bounds in the sense of A.D. Alexandrov. As a by-product we develop new tools in the theory of tangent cones of these spaces and obtain new characterization results which may be of independent interest.

Abstract

We generalize Kirszbraun's extension theorem for Lipschitz maps between (subsets of) euclidean spaces to metric spaces with upper or lower curvature bounds in the sense of A.D. Alexandrov. As a by-product we develop new tools in the theory of tangent cones of these spaces and obtain new characterization results which may be of independent interest.

Citations

47 citations in Web of Science®
44 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1997
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:26
Publisher:Birkhäuser
ISSN:1016-443X
Publisher DOI:https://doi.org/10.1007/s000390050018
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1466337
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0891.53046

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