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arXiv · 0803.1697

Markov convexity and local rigidity of distorted metrics

Manor Mendel·Assaf Naor
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Abstract

It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-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.

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Manor Mendel, Assaf Naor. 2010-07-26. Markov convexity and local rigidity of distorted metrics. https://doi.org/10.4171/jems%2F354

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