D. Ryabogin

activity

20092026

most citedA remark on the Mahler conjecture: local minimality of the unit cube

60 citations · 80 across the 17 of their papers we have counts for

collaborators

22 papers

math.MG2026

On determination of convex bodies by their section functions

Alexander Fish, Dmitry Ryabogin, Wen Rui Sun +1

For a convex body $K$ its parallel section function in the direction $θ \in S^{n - 1}$ is defined by $$A_{K,θ}(t) = \mathrm{vol}_{n-1} \left( K \cap \{ x \in \mathbb{R}^n ~ | ~ \langl…

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.FA2026

Zonoids whose polars are zonoids: the Banach--Mazur distance need not tend to one

Dmitry Ryabogin, Artem Zvavitch

For every $n \geq 2$ , we consider a Gaussian zonoid of revolution $Z_{n}$ arising from works of Vitale and Mathis. We prove that $Z_{n}^{*}$ is also a zonoid and compute the Banach--Mazur…

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 convex bodies with constant non-central sections

J. Haddad, D. Ryabogin

We prove that if $C$ is a symmetric convex body of revolution in $R^{4}$ containing the unit Euclidean ball $B_{4}$ , such that the sections of $C$ by hyperplanes tangen…

math.MG2023

On the maximal distance between the centers of mass of a planar convex body and its boundary

Fedor Nazarov, Dmitry Ryabogin, Vladyslav Yaskin

We prove that the length of the projection of the vector joining the centers of mass of a convex body on the plane and of its boundary to an arbitrary direction does not exceed $\f…