# Markov convexity and local rigidity of distorted metrics

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 1, page 287-337
- ISSN: 1435-9855

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topMendel, Manor, and Naor, Assaf. "Markov convexity and local rigidity of distorted metrics." Journal of the European Mathematical Society 015.1 (2013): 287-337. <http://eudml.org/doc/277644>.

@article{Mendel2013,

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.},

author = {Mendel, Manor, Naor, Assaf},

journal = {Journal of the European Mathematical Society},

keywords = {uniform convexity; Markov convexity; local regidity; tree metrics; Hamming cube; Lipschitz quotient; bilipschitz embeddings; Hamming cube; Markov convexity; tree metric; uniformly convex Banach space; Lipschitz quotient; bilipschitz embeddings},

language = {eng},

number = {1},

pages = {287-337},

publisher = {European Mathematical Society Publishing House},

title = {Markov convexity and local rigidity of distorted metrics},

url = {http://eudml.org/doc/277644},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Mendel, Manor

AU - Naor, Assaf

TI - Markov convexity and local rigidity of distorted metrics

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 1

SP - 287

EP - 337

AB - 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.

LA - eng

KW - uniform convexity; Markov convexity; local regidity; tree metrics; Hamming cube; Lipschitz quotient; bilipschitz embeddings; Hamming cube; Markov convexity; tree metric; uniformly convex Banach space; Lipschitz quotient; bilipschitz embeddings

UR - http://eudml.org/doc/277644

ER -

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