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

100%

Ostrovskii M.

Fundamenta Mathematicae

2014

tom 227

nr 1

85-95

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.

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Minimum congestion spanning trees of grids and discrete toruses

63%

Castejón A., Ostrovskii M.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 3

511-519

The paper is devoted to estimates of the spanning tree congestion for grid graphs and discrete toruses of dimensions two and three.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Fundamenta Mathematicae

2 Ostrovskii M.

1 Castejón A.

1 2014

1 2009

Wyniki wyszukiwania

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

Minimum congestion spanning trees of grids and discrete toruses