A universal Lipschitz extension property of Gromov hyperbolic spaces
Copyright policy )A universal Lipschitz extension property of Gromov hyperbolic spaces
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.
Primary 26B35, Secondary 54E35, 46B15, Lipschitz function, \(C\)-isometric embedding, 54E35, \(K\)-uniform measure, Harmonic analysis on homogeneous spaces, Mathematics - Metric Geometry, metric space of bounded geometry, FOS: Mathematics, Gromov hyperbolic space, 46B15, universal space, linear extension, metric space, Metric Geometry (math.MG), doubling metric space, Functional Analysis (math.FA), Mathematics - Functional Analysis, hyperbolic space, Special properties of functions of several variables, Hölder conditions, etc., Metric spaces, metrizability, simultaneous Lipschitz extension, doubling measure, 26B35, quasi-isometric embedding
Primary 26B35, Secondary 54E35, 46B15, Lipschitz function, \(C\)-isometric embedding, 54E35, \(K\)-uniform measure, Harmonic analysis on homogeneous spaces, Mathematics - Metric Geometry, metric space of bounded geometry, FOS: Mathematics, Gromov hyperbolic space, 46B15, universal space, linear extension, metric space, Metric Geometry (math.MG), doubling metric space, Functional Analysis (math.FA), Mathematics - Functional Analysis, hyperbolic space, Special properties of functions of several variables, Hölder conditions, etc., Metric spaces, metrizability, simultaneous Lipschitz extension, doubling measure, 26B35, quasi-isometric embedding
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