Markov convexity and local rigidity of distorted metrics

Manor Mendel, Assaf Naor

Type: Article

Publication Date: 2012-11-24

Citations: 39

DOI: https://doi.org/10.4171/jems/362

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.

Locations

Journal of the European Mathematical Society - View - PDF

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+	Metric Structures for Riemannian and Non-Riemannian Spaces	2007	Mikhael Gromov
+	Ramsey-like properties for bi-Lipschitz mappings of finite metric spaces	1992	Jiřı́ Matoušek
+	Geometric Nonlinear Functional Analysis	1999	Yoav Benyamini Joram Lindenstrauss
+	Sharp uniform convexity and smoothness inequalities for trace norms	1994	Keith Ball Eric A. Carlen Élliott H. Lieb
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