This is an announcement for the paper "On strict inclusions in hierarchies of convex bodies" by V.Yaskin.

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) $\mathcal I_l \not\subset \mathcal I_k$, $1\le k<l < n-3$.

Archive classification: math.FA

Mathematics Subject Classification: 52A20, 52A21, 46B04

Remarks: 10 pages

The source file(s), Yaskin.tex: 31833 bytes, is(are) stored in gzipped form as 0707.1471.gz with size 10kb. The corresponding postcript file has gzipped size 82kb.

Submitted from: vyaskin@math.ou.edu

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