On strict inclusions in hierarchies of convex bodies

V. Yaskin

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arXiv · 0707.1471

On strict inclusions in hierarchies of convex bodies

V. Yaskin

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Abstract

Let $\mathcal I_k$ be the class of convex $k$-intersection bodies in $\mathbb{R}^n$ (in the sense of Koldobsky) and $\mathcal I_k^m$ be the class of convex origin-symmetric bodies all of whose $m$-dimensional central sections are $k$-intersection bodies. We show that 1) $\mathcal I_k^m\not\subset \mathcal I_k^{m+1}$, $k+3\le m<n$, and 2) $\mathcal I_l \not\subset \mathcal I_k$, $1\le k<l < n-3$.

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BibTeX RIS

V. Yaskin. 2007-07-10. On strict inclusions in hierarchies of convex bodies. https://arxiv.org/abs/0707.1471

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