Andrii Arman

activity

20212026

most citedSmall volume bodies of constant width

1 citations · 2 across the 11 of their papers we have counts for

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5 papers · 1 filter

math.MG2024

On a Gallai-type problem and illumination of spiky balls and cap bodies

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

We show that any finite family of pairwise intersecting balls in $E^{n}$ can be pierced by $(3/2 + o (1))^{n}$ points improving the previously known estimate of $(2+o(1))^…

math.MG2024

Minimal dispersion on the cube and the torus

Andrii Arman, Alexander E. Litvak

We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion…

math.MG2024

Small Volume Bodies of Constant Width with Tetrahedral Symmetries

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

For every $n \geq 2$ , we construct a body $U_{n}$ of constant width $2$ in $E^{n}$ with small volume and symmetries of a regular $n$ -simplex. $U_{2}$ is the Reuleaux triangle. To…

math.MG2024★ 1 cited

Small volume bodies of constant width

Andrii Arman, Andriy Bondarenko, Fedor Nazarov +2

For every large enough $n$ , we explicitly construct a body of constant width $2$ that has volume less than $0. 9^{n} Vol (B^{n}$ ), where $B^{n}$ is the unit ba…

math.MG2024

On Hadwiger's covering problem in small dimensions

Andrii Arman, Andriy Bondarenko, Andriy Prymak

Let $H_{n}$ be the minimal number such that any $n$ -dimensional convex body can be covered by $H_{n}$ translates of interior of that body. Similarly $H_{n}^{s}$ is the corresponding quanti…