K. Tatarko

collaborators

6 papers

math.MG2026

The Spherical GrÃ¼nbaum Inequality

Sergii Myroshnychenko, Dmitry Ryabogin, Kateryna Tatarko +1

We prove an analogue of GrÃ¼nbaum'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 $Î¸\in \mathbb S^…

math.MG2026

On hyperbolic and functional analogues of questions of GrÃ¼nbaum 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.DG2026

A reverse isoperimetric inequality in three-dimensional space forms

Kostiantyn Drach, Gil Solanes, Kateryna Tatarko

A $I^»$ -convex body in a three-dimensional space form $M^{3} (c)$ of constant curvature $c$ is a compact convex set $K$ whose boundary $\partial K$ has normal curvatures bounded below…

math.DG2026

Stability of reverse isoperimetric inequalities in the plane: area, Cheeger, and inradius

Kostiantyn Drach, Kateryna Tatarko

In this paper, we present sharp stability results for various reverse isoperimetric problems in $R^{2}$ . Specifically, we prove the stability of the reverse isoperimetric ine…

math.MG2025

A solution to Bezdek's conjecture

Kostiantyn Drach, Kateryna Tatarko

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

math.MG2025

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…