S. Myroshnychenko

activity

20162026

most citedFunctional Response Designs via the Analytic Permutation Test

7 citations · 9 across the 15 of their papers we have counts for

collaborators

17 papers

math.MG2026

On convex bodies with rotationally symmetric planar projections

Sergii Myroshnychenko, Dmitry Ryabogin, Christos Saroglou

Let $n \geq 3$ and let $K \subset R^{n}$ be a convex body. For a two-dimensional linear subspace $P \subset R^{n}$ , let $K ∣ P$ be the orthogonal projection of $K$ onto $P$ . We…

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 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.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 $δ \in (0, 1)$ floating in a liquid of density $1$ , is uniquely determined by its surface of f…

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.MG2022

How far apart can the projection of the centroid of a convex body and the centroid of its projection be?

Sergii Myroshnychenko, Kateryna Tatarko, Vladyslav Yaskin

We show that there is a constant $D \approx 0.2016$ such that for every $n$ , every convex body $K \subset R^{n}$ , and every hyperplane $H \subset R^{n}$ , the distance bet…

math.MG2022★ 2 cited

Entropic exercises around the Kneser-Poulsen conjecture

Gautam Aishwarya, Irfan Alam, Dongbin Li +2

We develop an information-theoretic approach to study the Kneser--Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether Rényi entropies of in…

math.MG2020

Unique determination of ellipsoids by their dual volumes and the moment problem

Sergii Myroshnychenko, Kateryna Tatarko, Vladyslav Yaskin

Gusakova and Zaporozhets conjectured that ellipsoids in $R^{n}$ are uniquely determined (up to an isometry) by their Steiner polynomials. Petrov and Tarasov confirmed this co…

math.MG2020

On some characterizations of convex polyhedra

Sergii Myroshnychenko

This work provides two sufficient conditions in terms of sections or projections for a convex body to be a polytope. These conditions are necessary as well.

math.ST2020★ 7 cited

Functional Response Designs via the Analytic Permutation Test

Adam B Kashlak, Sergii Myroshnychenko, Susanna Spektor

Vast literature on experimental design extends from Fisher and Snedecor to the modern day. When data lies beyond the assumption of univariate normality, nonparametric methods inclu…

math.MG2017

Grünbaum's inequality for sections

Sergii Myroshnychenko, Matthew Stephen, Ning Zhang

We show \begin{align*} \frac{ \int_{E \cap θ^+} f(x) dx }{ \int_E f(x) dx } \geq \left(\frac{k γ+1}{(n+1) γ+1}\right)^{\frac{k γ+1}γ} \end{align*} for all $k$ -dimensional subspaces…

math.MG2017

On recognizing shapes of polytopes from their shadows

Sergii Myroshnychenko

Let $P$ and $Q$ be two convex polytopes both contained in the interior of an Euclidean ball $r B^{d}$ . We prove that $P = Q$ provided that their sight cones from any point on…

math.MG2016

On a functional equation related to a pair of hedgehogs with congruent projections

Sergii Myroshnychenko

Hedgehogs are geometrical objects that describe the Minkowski differences of arbitrary convex bodies in the Euclidean space $E^{n}$ . We prove that two hedgehogs in $\mathbb{…

math.MG2016

Star bodies with completely symmetric sections

Sergii Myroshnychenko, Dmitry Ryabogin, Christos Saroglou

We say that a star body $K$ is completely symmetric if it has centroid at the origin and its symmetry group $G$ forces any ellipsoid whose symmetry group contains $G$ , to be a ball…

math.MG2016

On polytopes with congruent projections or sections

Sergii Myroshnychenko, Dmitry Ryabogin

Let $2 \leq k \leq d - 1$ and let $P$ and $Q$ be two convex polytopes in $E^{d}$ . Assume that their projections, $P ∣ H$ , $Q ∣ H$ , onto every $k$ -dimensional subspace $H$ , are congru…