This is an announcement for the paper "Metric spaces with linear extensions preserving Lipschitz condition" by A. Brudnyi and Yu. Brudnyi.

Abstract: We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor controlled by \lambda(M). We prove that \lambda(M) is finite for several important classes of metric spaces. These include metric trees of arbitrary cardinality, groups of polynomial growth, some groups of exponential growth and certain classes of Riemannian manifolds of bounded geometry. On the other hand we construct an example of a Riemann surface M of bounded geometry for which \lambda(M)=\infty.

Archive classification: Metric Geometry; Functional Analysis

Mathematics Subject Classification: 26B35; 54E35; 46B15

Remarks: 71 pages

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Submitted from: albru@math.ucalgary.ca

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