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math.MG2026
Optimal partial plank coverings
Egor Bakaev, Alexander Polyanskii
A plank of width in a Euclidean space is the set of points lying between two parallel hyperplanes at distance from each other. Bang's theorem says that if a family of plank…
math.MG2026
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…
math.MG2024
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…