Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on $ k$-intersection bodies

Author: Jared Schlieper
Journal: Proc. Amer. Math. Soc. 135 (2007), 2081-2088
MSC (2000): Primary 46B04
Published electronically: February 2, 2007
MathSciNet review: 2299484
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Abstract: The concept of an intersection body is central for the dual Brunn-Minkowski theory and has also played an important role in the solution of the Busemann-Petty problem. A more general concept of $ k$-intersection bodies is related to the generalization of the Busemann-Petty problem. In this note, we compare classes of $ k$-intersection bodies for different $ k$ and examine the conjecture that these classes increase with $ k$. In particular, we construct a $ 4$-intersection body that is not a $ 2$-intersection body.

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Jared Schlieper
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Received by editor(s): March 6, 2006
Published electronically: February 2, 2007
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.