K. Tatarko

activity

20182026

most citedReverse isoperimetric problems under curvature constraints

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

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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…