Egor Bakaev

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20232026

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math.MG2026

Volume stability of plank covers

Egor Bakaev, Amir Yehudayoff

We prove a longstanding conjecture of András Bezdek on the stability of plank covers of the planar disk $D$ . If a sufficiently small disk $ε D$ is removed, then every fin…

math.MG2026

Optimal partial plank coverings

Egor Bakaev, Alexander Polyanskii

A plank of width $w$ in a Euclidean space is the set of points lying between two parallel hyperplanes at distance $w$ from each other. Bang's theorem says that if a family of plank…

math.MG2026

A simplex-based measure of symmetry

Egor Bakaev, Amir Yehudayoff

For compact convex sets $L, K \subset R^{n}$ , denote by $λ_{K} (L)$ the smallest size of a homothet of $K$ that contains $L$ . We define a measure of symmetry based on the $n$ -si…

math.MG2026

A note on the affine plank conjecture

Egor Bakaev, Amir Yehudayoff

In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in $R^{d}$ is covered by planks, then the total relative width of the planks is at leas…