Geometric & Functional Analysis GAFA

, Volume 10, Issue 6, pp 1527–1553

Extensions of Lipschitz maps into Hadamard spaces

  • U. Lang
  • B. Pavlović
  • V. Schroeder

DOI: 10.1007/PL00001660

Cite this article as:
Lang, U., Pavlović, B. & Schroeder, V. GAFA, Geom. funct. anal. (2000) 10: 1527. doi:10.1007/PL00001660

Abstract.

We prove that every \( \lambda \)-Lipschitz map \( f : S \to Y \) defined on a subset of an arbitrary metric space X possesses a \( c \lambda \)-Lipschitz extension \( \bar{f} : X \to Y \) for some \( c = c(Y) \ge 1 \) provided Y is a Hadamard manifold which satisfies one of the following conditions: (i) Y has pinched negative sectional curvature, (ii) Y is homogeneous, (iii) Y is two-dimensional. In case (i) the constant c depends only on the dimension of Y and the pinching constant, in case (iii) one may take \( c = 4\sqrt{2} \). We obtain similar results for large classes of Hadamard spaces Y in the sense of Alexandrov.

Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • U. Lang
    • 1
  • B. Pavlović
    • 2
  • V. Schroeder
    • 3
  1. 1.Departement Mathematik, ETH Zentrum, Rämistrasse 101, CH-8092 Zürich, Switzerland, e-mail: lang@math.ethz.chCH
  2. 2.Institute of Mathematics, Belgrade, Yugoslavia, and School of Mathematics, Trinity College, Dublin 2, Ireland, e-mail: pavlovic@maths.tcd.ieIE
  3. 3.Institut für Mathematik, Universität Zürich-Irchel, Winterthurer Strasse 190, CH-8057 Zürich, Switzerland, e-mail: vschroed@math.unizh.chCH