Geometric & Functional Analysis GAFA

, Volume 7, Issue 3, pp 535–560

Kirszbraun's Theorem and Metric Spaces of Bounded Curvature

  • U. Lang
  • V. Schroeder

DOI: 10.1007/s000390050018

Cite this article as:
Lang, U. & Schroeder, V. GAFA, Geom. funct. anal. (1997) 7: 535. doi:10.1007/s000390050018


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.

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