Author

D. Ryabogin

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Preprint Oct 2026

On determination of convex bodies by their section functions

For a convex body $K$ its parallel section function in the direction $\theta\in S^{n-1}$ is defined by $$A_{K,\theta}(t) = \mathrm{vol}_{n-1} \left( K \cap \{ x \in \mathbb{R}^n ~ | ~ \langle x, \theta \rangle = t \} \right) .$$ We study to what extent the body $K$ is determined by partial information about these funct...

A. Fish, D. Ryabogin, Wen-Rui Sun et al. · 0 citations

Preprint Jul 2026

The Spherical Gr\"unbaum Inequality

We prove an analogue of Gr\"unbaum's inequality on the sphere. Let $n \geq 3$ and let $K$ be a convex body on $\mathbb S^{n-1}\subset \mathbb R^n$ with centroid at $\theta\in \mathbb S^{n-1}$. Then for any $u\in \mathbb S^{n-1}$ that is orthogonal to $\theta$ we have $$\sigma(K\cap u^+) \ge \left(1-\frac{1}{n}\right)^{...

S. Myroshnychenko, D. Ryabogin, Kateryna Tatarko et al. · 0 citations