S. Myroshnychenko

activity

20242026

collaborators

6 papers

math.MG2026

Area Minimization Among Group-Invariant Planar Convex Bodies of Constant Width

Javier Falco, Sergii Myroshnychenko

The classical Blaschke--Lebesgue theorem identifies the Reuleaux triangle as the planar convex body of constant width with minimum area. We investigate this extremal problem under…

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.MG2026

Uniqueness of Flotation and Buoyancy Surfaces for Convex Polytopes

Susanna Dann, Orli Herscovici, Sergii Myroshnychenko

We prove that a convex polytope $P \subset R^{d}$ , $d \geq 2$ , of uniform density $I^´ \in (0, 1)$ floating in a liquid of density $1$ , is uniquely determined by its surface of…

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…

math.MG2024

Answers to questions of GrÃ¼nbaum 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…