V. Yaskin

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math.MG2026

Polyhedral Subspaces of $L_{p}$ and Polars of Zonotopes

Vladyslav Yaskin

Let $K$ be an origin-symmetric full-dimensional convex polytope in $R^{n}$ , $n \geq 3$ . We show that, for $- n + 3 < p < 1$ , the normed space $(R^{n}, ∥ \cdot ∥_{K})$ embeds in $L_…

math.MG2026

The Spherical GrÃ¼nbaum Inequality

Sergii Myroshnychenko, Dmitry Ryabogin, Kateryna Tatarko +1

We prove an analogue of GrÃ¼nbaum'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 $Î¸\in \mathbb S^…

math.MG2024

A generalization of GrÃ¼nbaum's inequality

Brayden Letwin, Vladyslav Yaskin

GrÃ¼nbaum'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…

Polyhedral Subspaces of Lp​ and Polars of Zonotopes

The Spherical GrÃ¼nbaum Inequality

A generalization of GrÃ¼nbaum's inequality

Polyhedral Subspaces of $L_{p}$ and Polars of Zonotopes