K. Tatarko

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20182026

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8 papers · 1 filter

math.MG2026

The Spherical Grünbaum Inequality

Sergii Myroshnychenko, Dmitry Ryabogin, Kateryna Tatarko +1

We prove an analogue of Grünbaum's inequality on the sphere. Let $n \geq 3$ and let $K$ be a convex body on $S^{n - 1} \subset R^{n}$ with centroid at $θ\in \mathbb S^{n…

math.MG2026

On hyperbolic and functional analogues of questions of Grünbaum and Loewner

Yu Huang, Sergii Myroshnychenko, Kateryna Tatarko +1

Myroshnychenko, Tatarko, and Yaskin constructed a body $K$ in $R^{n}$ , $n \geq 5$ , with the property that there is exactly one hyperplane $H$ passing through $c (K)$ , the cen…

math.MG2025

A solution to Bezdek's conjecture

Kostiantyn Drach, Kateryna Tatarko

For a given $λ > 0$ , a convex body in $R^{n}$ is $λ$ -convex if it is the intersection of (finitely or infinitely many) balls of radius $1/ λ$ . In this note, we show that among a…

math.MG2024

Answers to questions of Grünbaum and Loewner

S. Myroshnychenko, K. Tatarko, V. Yaskin

We construct a convex body $K$ in $R^{n}$ , $n \geq 5$ , with the property that there is exactly one hyperplane $H$ passing through $c (K)$ , the centroid of $K$ , such that the…

math.MG2024

Stability of simplex slicing

Serhii Myroshnychenko, Colin Tang, Kateryna Tatarko +1

We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary (not…

math.MG2023★ 1 cited

Reverse isoperimetric problems under curvature constraints

Kostiantyn Drach, Kateryna Tatarko

In this paper we solve several reverse isoperimetric problems in the class of $λ$ -convex bodies, i.e., convex bodies whose curvature at each point of their boundary is bounded belo…