This is an announcement for the paper "Metric spaces nonembeddable into Banach spaces with the property and thick families of geodesics" by Mikhail Ostrovskii.

Abstract: We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod'ym 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-Nikod'ym property contains a bilipschitz image of a thick family of geodesics.

Archive classification: math.MG math.FA

Mathematics Subject Classification: Primary 30L05, Secondary: 46B22, 46B85

Submitted from: ostrovsm@stjohns.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1312.5381

or

http://arXiv.org/abs/1312.5381