83 citations · 542 across the 80 of their papers we have counts for
15 papers · 1 filter
Equipartition of a measure by -invariant fans
R. N. Karasev
We prove a result about partitioning an absolute continuous measure in into 2d equal parts by a system of cones with common vertex, where is an odd prime power. T…
A simpler proof of the Boros-Füredi-Bárány-Pach-Gromov theorem
R. N. Karasev
A short and almost elementary proof of the Boros-Füredi-Bárány-Pach-Gromov theorem on the multiplicity of covering by simplices in is given.
Equipartition of several measures
R. N. Karasev
We prove several results of the following type: any measures in can be partitioned simultaneously into equal parts by a convex partition (this particular resu…
A topological central point theorem
R. N. Karasev
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem a…
Extensions of theorems of Rattray and Makeev
Pavle Blagojević, Roman Karasev
We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold for several maps, measures, or functions simultaneously, when we consider orthonorma…
Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
V. L. Dol'nikov, R. N. Karasev
In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on , and improve bounds on the number in the ana…