A metric space has the universal Lipschitz extension property if for an arbitrary metric space and every subspace of isometric to a subspace of there exists a continuous linear extension of Banach-valued Lipschitz functions on to those on all of . We show that the finite direct sum of Gromov hyperbolic spaces of bounded geometry is universal in the sense of this definition.
Cite this article
Alexander Brudnyi, Yuri Brudnyi, A universal Lipschitz extension property of Gromov hyperbolic spaces. Rev. Mat. Iberoam. 23 (2007), no. 3, pp. 861–896DOI 10.4171/RMI/517