83 citations · 542 across the 80 of their papers we have counts for
4 papers · 2 filters
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…
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…
A measure of non-convexity in the plane and the Minkowski sum
R. N. Karasev
In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decreas…
A note on Makeev's conjectures
R. N. Karasev
A counterexample is given for the Knaster-like conjecture of Makeev for functions on . Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a…