JournalsjemsVol. 15, No. 1pp. 287–337

Markov convexity and local rigidity of distorted metrics

  • Manor Mendel

    The Open University of Israel, Raanana, Israel
  • Assaf Naor

    New York University, United States
Markov convexity and local rigidity of distorted metrics cover
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Abstract

It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type pp if and only if it is Markov pp-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.

Cite this article

Manor Mendel, Assaf Naor, Markov convexity and local rigidity of distorted metrics. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 287–337

DOI 10.4171/JEMS/362