83 citations · 542 across the 80 of their papers we have counts for
81 papers
An isoperimetric inequality for mean shadow
Roman Karasev, Anton Petrunin, Alexander Plakhov
We prove an isoperimetric inequality in terms of the mean shadow area.
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…
Systolic inequalities and chromatic number
Alexander Kamal, Roman Karasev
We show that the discrete versions of the systolic inequality that estimate the number of vertices of a simplicial complex from below have substantial applications to graphs, the o…
Convex bodies with all characteristics planar
Roman Karasev, Anastasiia Sharipova
We show that smooth and strongly convex bodies in the symplectic for with all characteristics planar, or all outer billiard trajectories planar are affine sy…