Revista Matemática Iberoamericana


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Volume 23, Issue 3, 2007, pp. 861–896
DOI: 10.4171/RMI/517

Published online: 2007-12-31

A universal Lipschitz extension property of Gromov hyperbolic spaces

Alexander Brudnyi[1] and Yuri Brudnyi[2]

(1) University of Calgary, Canada
(2) Technion - Israel Institute of Technology, Haifa, Israel

A metric space $U$ has the universal Lipschitz extension property if for an arbitrary metric space $M$ and every subspace $S$ of $M$ isometric to a subspace of $U$ 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.

Keywords: Metric space, Lipschitz function, linear extension

Brudnyi Alexander, Brudnyi Yuri: A universal Lipschitz extension property of Gromov hyperbolic spaces. Rev. Mat. Iberoam. 23 (2007), 861-896. doi: 10.4171/RMI/517