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2013 | 1 | 163-199

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Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

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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.


  • Mathematics and Computer Science Department,
    The Open University of Israel, 1 University Road,
    P.O. Box 808, Raanana 43107, Israel
  • Courant Institute of Mathematical Sciences,
    New York University, 251 Mercer Street,
    New York NY 10012, USA


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