## Extendability of Large-Scale Lipschitz Maps

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**351**(1999), 3975-3988 Request permission

## 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.## References

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## Additional Information

**Urs Lang**- Affiliation: Departement Mathematik, Eidgen Technische Hochschule Zentrum, CH-8092 Zürich, Switzerland
- Email: lang@math.ethz.ch
- Received by editor(s): August 8, 1997
- Published electronically: February 8, 1999
- Additional Notes: Supported by the Swiss National Science Foundation.
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1698373