A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces

Details A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces

2006-01-10

arxiv.org/abs/math/0601205v1

Mathematics

Metric Geometry

31 pages

Scientific paper

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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