On strict inclusions in hierarchies of convex bodies

Details On strict inclusions in hierarchies of convex bodies On strict inclusions in hierarchies of convex bodies

2007-07-10

arxiv.org/abs/0707.1471v1

Mathematics

Metric Geometry

10 pages

Scientific paper

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

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