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Kirszbraun's Theorem and Metric Spaces of Bounded Curvature

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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.

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Authors and Affiliations

  1. U. Lang, Department of Mathematics, Stanford University, Stanford, CA 94305, USA, e-mail: lang@math.stanford.edu, , , , , , US

    U. Lang

  2. V. Schroeder, Institut für Mathematik, Universität Zürich-Irchel; Winterthurer Str. 190, CH-8057 Zürich, e-mail: vschroed@math.unizh.ch, , , , , , CH

    V. Schroeder

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  1. U. Lang
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  2. V. Schroeder
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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

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  • DOI: https://doi.org/10.1007/s000390050018

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