Markov convexity and local rigidity of distorted metrics

Manor Mendel, Assaf Naor
2008 Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08  
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.
doi:10.1145/1377676.1377686 dblp:conf/compgeom/MendelN08 fatcat:udnwcsoudzbj7dbyxekbalqune