13 citations · 18 across the 20 of their papers we have counts for
26 papers
On determination of convex bodies by their section functions
Alexander Fish, Dmitry Ryabogin, Wen Rui Sun +1
For a convex body its parallel section function in the direction is defined by $$A_{K,θ}(t) = \mathrm{vol}_{n-1} \left( K \cap \{ x \in \mathbb{R}^n ~ | ~ \langl…
Polyhedral Subspaces of and Polars of Zonotopes
Vladyslav Yaskin
Let be an origin-symmetric full-dimensional convex polytope in , . We show that, for , the normed space embeds in $L_…
The Spherical Grünbaum Inequality
Sergii Myroshnychenko, Dmitry Ryabogin, Kateryna Tatarko +1
We prove an analogue of Grünbaum's inequality on the sphere. Let and let be a convex body on with centroid at $θ\in \mathbb S^{n…
A generalization of Grünbaum's inequality
Brayden Letwin, Vladyslav Yaskin
Grünbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of t…
On separably integrable symmetric convex bodies
Vladyslav Yaskin, Bartłomiej Zawalski
An infinitely smooth symmetric convex body is called -separably integrable, , if its -dimensional isotropic volume function $V_{K,H}(t)=\math…
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…