111 citations
- Atilim UniversityTR4 papers
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- McMaster UniversityCA3 papers
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- Vologda State UniversityRU3 papers
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6 papers · 1 filter
The Aleksandrov problem for origin-symmetric polytopes
Yiming Zhao
The Aleksandrov integral curvature and its corresponding characterization problem---the Aleksandrov problem---were recently introduced by Huang, Lutwak, Yang, and Zhang…
Regular Finite Decomposition Complexity
Daniel Kasprowski, Andrew Nicas, David Rosenthal
We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov's finite asymptotic dimension and is motivated by the concept of fini…
Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs
Mikhail Ostrovskii
We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of dia…
Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics
Mikhail Ostrovskii
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…
Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space
M. I. Ostrovskii
The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to…
Fixed points of holomorphic transformations of operator balls
M. I. Ostrovskii, V. S. Shulman, L. Turowska
A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded re…