, Volume 7, Issue 3, pp 535-560

Kirszbraun's Theorem and Metric Spaces of Bounded Curvature

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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.