Markov convexity and local rigidity of distorted metrics

Details Markov convexity and local rigidity of distorted metrics Markov convexity and local rigidity of distorted metrics

2008-03-12

arxiv.org/abs/0803.1697v2

Mathematics

Metric Geometry

47 pages, full version, replacing the previous version which was an announcement

Scientific paper

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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