83 citations · 542 across the 80 of their papers we have counts for
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Measure Partitions Using Hyperplanes with Fixed Directions
Roman Karasev, Edgardo Roldán-Pensado, Pablo Soberón
We study nested partitions of obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously…
Bang's problem and symplectic invariants
Arseniy Akopyan, Roman Karasev, Fedor Petrov
We consider the Tarski--Bang problem about covering of convex bodies by planks. The results of this kind give a lower bound on the sum of widths of planks (regions between a pair o…
Bounds for Pach's selection theorem and for the minimum solid angle in a simplex
Roman Karasev, Jan Kynčl, Pavel Paták +2
We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer there is a constant such that whenever $X_1,..., X…
Elementary approach to closed billiard trajectories in asymmetric normed spaces
Arseniy V. Akopyan, Alexey M. Balitskiy, Roman N. Karasev +1
We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a…