Markov convexity and local rigidity of distorted metrics

Mendel, 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 -