It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type if and only if it is Markov -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. 287–337DOI 10.4171/JEMS/362