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Optimal partial plank coverings
Egor Bakaev, Alexander Polyanskii
The paper investigates how to place planks of a fixed total width to cover the largest possible volume of a convex body, proving that for a Euclidean ball and for any planar convex…
Triangle covering problems and the Viterbo inequality in the plane
Alexey Balitskiy, Ivan Mitrofanov, Alexander Polyanskii
We review a certain problem on covering triangles in the plane. Equivalently, it can be viewed as a family of 'isobilliard' inequalities in convex shapes, and as a special case of…
Tight colorful no-dimensional Tverberg theorem
Polina Barabanshchikova, Grigory Ivanov, Alexander Polyanskii
We study colorful no-dimensional Tverberg-type problems and obtain several optimal results. A colorful no-dimensional Tverberg-type theorem provides a bound on a radius such th…