A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces
Metric Geometry
2007-05-23 v1 Functional Analysis
Abstract
A metric space has the universal Lipschitz extension property if for each subspace S embedded quasi-isometrically into an arbitrary metric space M there exists a continuous linear extension of Banach-valued Lipschitz functions on S to those on all of M. We show that the finite direct sum of Gromov hyperbolic spaces of bounded geometry is universal in the sense of this definition.
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Cite
@article{arxiv.math/0601205,
title = {A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces},
author = {A. Brudnyi and Yu. Brudnyi},
journal= {arXiv preprint arXiv:math/0601205},
year = {2007}
}
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31 pages