Metric spaces nonembeddable into Banach spaces with the Radon–Nikodým property and thick families of geodesics
Volume 227 / 2014
Fundamenta Mathematicae 227 (2014), 85-95
MSC: Primary 30L05; Secondary 46B22, 46B85.
DOI: 10.4064/fm227-1-6
Abstract
We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon–Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger–Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon–Nikodým property contains a bilipschitz image of a thick family of geodesics.
