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Geometric & Functional Analysis GAFA

, Volume 10, Issue 6, pp 1527–1553 | Cite as

Extensions of Lipschitz maps into Hadamard spaces

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

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.

Keywords

Large Classis Sectional Curvature Lipschitz Extension Negative Sectional Curvature Hadamard Space 
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 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

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