Geometric & Functional Analysis GAFA

, Volume 7, Issue 3, pp 535–560 | Cite as

Kirszbraun's Theorem and Metric Spaces of Bounded Curvature

  • U. Lang
  • V. Schroeder

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.

Keywords

Euclidean Space Bound Curvature Lower Curvature Independent Interest Characterization Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • U. Lang
    • 1
  • V. Schroeder
    • 2
  1. 1.U. Lang, Department of Mathematics, Stanford University, Stanford, CA 94305, USA, e-mail: lang@math.stanford.eduUS
  2. 2.V. Schroeder, Institut für Mathematik, Universität Zürich-Irchel; Winterthurer Str. 190, CH-8057 Zürich, e-mail: vschroed@math.unizh.chCH

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