K. Tatarko

activity

20182026

most citedReverse isoperimetric problems under curvature constraints

1 citations · 1 across the 10 of their papers we have counts for

collaborators

13 papers

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.DG2026

A reverse isoperimetric inequality in three-dimensional space forms

Kostiantyn Drach, Gil Solanes, Kateryna Tatarko

A $λ$ -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 b…

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.DG2024

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.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…

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

Curvature functionals on convex bodies

Kateryna Tatarko, Elisabeth M. Werner

We investigate the weighted $L_{p}$ affine surface areas which appear in the recently established $L_{p}$ Steiner formula of the $L_{p}$ Brunn Minkowski theory. We show that they are val…

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.DG2018

A Steiner formula in the $L_{p}$ Brunn Minkowski theory

Kateryna Tatarko, Elisabeth M. Werner

We prove an analogue of the classical Steiner formula for the $L_{p}$ affine surface area of a Minkowski outer parallel body for any real parameters $p$ . We show that the classical S…

math.DG2018

A sausage body is a unique solution for a reverse isoperimetric problem

Roman Chernov, Kostiantyn Drach, Kateryna Tatarko

We consider the class of $λ$ -concave bodies in $R^{n + 1}$ ; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/λ…

The Spherical Grünbaum Inequality

On hyperbolic and functional analogues of questions of Grünbaum and Loewner

A reverse isoperimetric inequality in three-dimensional space forms

A solution to Bezdek's conjecture

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

Answers to questions of Grünbaum and Loewner

Stability of simplex slicing

Reverse isoperimetric problems under curvature constraints

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

Curvature functionals on convex bodies

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

A Steiner formula in the Lp​ Brunn Minkowski theory

A sausage body is a unique solution for a reverse isoperimetric problem

A Steiner formula in the $L_{p}$ Brunn Minkowski theory