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- Moscow Institute of Physics and TechnologyRU332 papers
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42 papers · 1 filter
Rogers's proof of Vaaler's theorem
Roman Karasev
We note that an argument by Rogers (1958) gives a proof of Vaaler's theorem (1979) about sections of the cube and allows certain generalizations of the theorem.
Weak -nets for polynomial superlevel sets
Pablo González-Mazón, Alfredo Hubard, Roman Karasev
We prove that for any Borel probability measure on there exists a set of points such that any -variate quadratic polynomial th…
Symplectic polarity and Mahler's conjecture
Mark Berezovik, Roman Karasev
We state a conjecture about the volume of symplectically self-polar convex bodies and show that it is equivalent to Mahler's conjecture concerning the volume of a convex body and i…
Extensions of polynomial plank covering theorems
Alexey Glazyrin, Roman Karasev, Alexandr Polyanskii
We prove a complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to…
Local-to-global Urysohn width estimates
Alexey Balitskiy, Aleksandr Berdnikov
The notion of the Urysohn -width measures to what extent a metric space can be approximated by a -dimensional simplicial complex. We investigate how local Urysohn width bound…
A cap covering theorem
Alexandr Polyanskii
A cap of spherical radius on a unit -sphere is the set of points within spherical distance from a given point on the sphere. Let be a finite set of caps…