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arXiv · 1312.5381

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

Mikhail Ostrovskii
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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.

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Mikhail Ostrovskii. 2014-04-04. Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics. https://doi.org/10.4064/fm227-1-6

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