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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Extendability of Large-Scale Lipschitz Maps


Author: Urs Lang
Journal: Trans. Amer. Math. Soc. 351 (1999), 3975-3988
MSC (1991): Primary 53C20; Secondary 51Kxx, 20F32
DOI: https://doi.org/10.1090/S0002-9947-99-02265-5
Published electronically: February 8, 1999
MathSciNet review: 1698373
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Abstract: Let $X,Y$ be metric spaces, $S$ a subset of $X$, and $f \colon S \to Y$ a large-scale lipschitz map. It is shown that $f$ possesses a large-scale lipschitz extension $\bar f \colon X \to Y$ (with possibly larger constants) if $Y$ is a Gromov hyperbolic geodesic space or the cartesian product of finitely many such spaces. No extension exists, in general, if $Y$ is an infinite-dimensional Hilbert space. A necessary and sufficient condition for the extendability of a lipschitz map $f \colon S \to Y$ is given in the case when $X$ is separable and $Y$ is a proper, convex geodesic space.


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Additional Information

Urs Lang
Affiliation: Departement Mathematik, Eidgen Technische Hochschule Zentrum, CH-8092 Zürich, Switzerland
Email: lang@math.ethz.ch

DOI: https://doi.org/10.1090/S0002-9947-99-02265-5
Received by editor(s): August 8, 1997
Published electronically: February 8, 1999
Additional Notes: Supported by the Swiss National Science Foundation.
Article copyright: © Copyright 1999 American Mathematical Society