JournalsrmiVol. 23, No. 3pp. 861–896

A universal Lipschitz extension property of Gromov hyperbolic spaces

  • Alexander Brudnyi

    University of Calgary, Canada
  • Yuri Brudnyi

    Technion - Israel Institute of Technology, Haifa, Israel
A universal Lipschitz extension property of Gromov hyperbolic spaces cover
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Abstract

A metric space UU has the universal Lipschitz extension property if for an arbitrary metric space MM and every subspace SS of MM isometric to a subspace of UU there exists a continuous linear extension of Banach-valued Lipschitz functions on SS to those on all of MM. 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. 861–896

DOI 10.4171/RMI/517