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.
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Submitted: June 1996, final version: November 1996
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Lang, U., Schroeder, V. Kirszbraun's Theorem and Metric Spaces of Bounded Curvature. GAFA, Geom. funct. anal. 7, 535–560 (1997). https://doi.org/10.1007/s000390050018