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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On strict inclusions in hierarchies of convex bodies


Author: Vladyslav Yaskin
Journal: Proc. Amer. Math. Soc. 136 (2008), 3281-3291
MSC (2000): Primary 52A20, 52A21, 46B04
Published electronically: May 1, 2008
MathSciNet review: 2407094
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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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Additional Information

Vladyslav Yaskin
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: vyaskin@math.ou.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09424-0
PII: S 0002-9939(08)09424-0
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.