Spectral calculus and lipschitz extension for barycentric metric spaces dedicated to nigel kalton

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)163-199
Number of pages37
JournalAnalysis and Geometry in Metric Spaces
Volume1
Issue number1
DOIs
StatePublished - 2013

Keywords

  • Cat (0) metric spaces
  • Lipschitz extension
  • Markov cotype
  • Nonlinear spectral gaps

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Applied Mathematics

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