On strict inclusions in hierarchies of convex bodies
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- by Vladyslav Yaskin PDF
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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) $\mathcal I_l \not \subset \mathcal I_k$, $1\le k<l < n-3$.References
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Additional Information
- Vladyslav Yaskin
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- MR Author ID: 650371
- Email: vyaskin@math.ou.edu
- Received by editor(s): July 10, 2007
- Published electronically: May 1, 2008
- Additional Notes: The author was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953. Part of this work was done when the author was visiting Université de Marne-la-Vallée.
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3281-3291
- MSC (2000): Primary 52A20, 52A21, 46B04
- DOI: https://doi.org/10.1090/S0002-9939-08-09424-0
- MathSciNet review: 2407094