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 language | English |
|---|---|
| Pages (from-to) | 163-199 |
| Number of pages | 37 |
| Journal | Analysis and Geometry in Metric Spaces |
| Volume | 1 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2013 |
Bibliographical note
Funding Information:We are grateful to the anonymous referees for their helpful suggestions. M. M. was supported by ISF grants 221/07 and 93/11, BSF grant 2010021, and NSF grant CCF-0832797. Part of this work was completed while M. M. was a member of the Institute for Advanced Study at Princeton, NJ. A. N. was supported by NSF grant CCF-0832795, BSF grant 2010021, the Packard Foundation and the Simons Foundation. Part of this work was completed while A. N. was visiting Universit? Pierre et Marie Curie, Paris, France.
Publisher Copyright:
© Versita sp. z o.o.
Keywords
- Cat (0) metric spaces
- Lipschitz extension
- Markov cotype
- Nonlinear spectral gaps