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

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.

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