Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics

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 any thick family of geodesics is not 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.

References in corpus (2)

• Radon-Nikodým property and thick families of geodesics
• Coarse differentiation and quantitative nonembeddability for Carnot groups