Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

• Autorzy: Manor Mendel , Assaf Naor
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Markov cotype; Lipschitz extension; CAT (0) metric spaces; nonlinear spectral gaps

Kategorie tematyczne

• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 46B85: Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science
• 54C20: Extension of maps

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 163-199

Daty

otrzymano

2013-01-21

zaakceptowano

2013-05-12

online

2013-05-28

Twórcy

autor

Manor Mendel

• Mathematics and Computer Science Department,
  The Open University of Israel, 1 University Road,
  P.O. Box 808, Raanana 43107, Israel

autor

Assaf Naor

• Courant Institute of Mathematical Sciences,
  New York University, 251 Mercer Street,
  New York NY 10012, USA

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Identyfikatory

DOI

10.2478/agms-2013-0003