Markov convexity and local rigidity of distorted metrics
Metric Geometry
2012-12-03 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.0803.1697,
title = {Markov convexity and local rigidity of distorted metrics},
author = {Manor Mendel and Assaf Naor},
journal= {arXiv preprint arXiv:0803.1697},
year = {2012}
}
Comments
47 pages, full version, replacing the previous version which was an announcement