7 citations · 8 across the 3 of their papers we have counts for
5 papers · 1 filter
An isoperimetric inequality for mean shadow
Roman Karasev, Anton Petrunin, Alexander Plakhov
We prove an isoperimetric inequality in terms of the mean shadow area.
Convex fair partitions into an arbitrary number of pieces
Arseniy Akopyan, Sergey Avvakumov, Roman Karasev
We prove that any convex body in the plane can be partitioned into convex parts of equal areas and perimeters for any integer ; this result was previously known for pri…
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…
Borsuk-Ulam type theorems for metric spaces
Arseniy Akopyan, Roman Karasev, Alexey Volovikov
In this paper we study the problems of the following kind: For a pair of topological spaces and find sufficient conditions that under every continuous map a pa…
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…