83 citations · 542 across the 80 of their papers we have counts for
5 papers · 2 filters
Topology of geometric joins
Imre Barany, Andreas F. Holmsen, Roman Karasev
We consider the geometric join of a family of subsets of the Euclidean space. This is a construction frequently used in the (colorful) Carathéodory and Tverberg theorems, and their…
Covering dimension using toric varieties
Roman Karasev
In this paper we deduce the Lebesgue and the Knaster--Kuratowski--Mazurkiewicz theorems on the covering dimension, as well as their certain generalizations, from some simple facts…
Another ham sandwich in the plane
Alexey Balitskiy, Alexey Garber, Roman Karasev
We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from arbitrary k-fan when k is odd and in some cases when k is eve…
Convex Equipartitions: The Spicy Chicken Theorem
Roman Karasev, Alfredo Hubard, Boris Aronov
We show that, for any prime power n and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into n convex sets with equal volumes and…
From Symplectic Measurements to the Mahler Conjecture
Shiri Artstein-Avidan, Roman Karasev, Yaron Ostrover
In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains, and Mahler'…