Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

Manor Mendel ; Assaf Naor

Analysis and Geometry in Metric Spaces, Tome 1 (2013), p. 163-199 / Harvested from The Polish Digital Mathematics Library

Résumé

The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.

Détail

Publié le : 2013-01-01

Zbl 1297.54037

EUDML-ID : urn:eudml:doc:266565

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