A universal Lipschitz extension property of Gromov hyperbolic spaces

Abstract

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.