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Counterexamples to convexity of $ k$-intersection bodies


Author: Vladyslav Yaskin
Journal: Proc. Amer. Math. Soc. 142 (2014), 4355-4363
MSC (2010): Primary 52A20
DOI: https://doi.org/10.1090/S0002-9939-2014-12254-4
Published electronically: August 14, 2014
MathSciNet review: 3267003
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Abstract: It is a well-known result due to Busemann that the intersection body of an origin-symmetric convex body is also convex. Koldobsky introduced the notion of $ k$-intersection bodies. We show that the $ k$-intersection body of an origin-symmetric convex body is not necessarily convex if $ k>1$.


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Additional Information

Vladyslav Yaskin
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: vladyaskin@math.ualberta.ca

DOI: https://doi.org/10.1090/S0002-9939-2014-12254-4
Keywords: Convex bodies, star bodies, $k$-intersection bodies
Received by editor(s): February 3, 2013
Published electronically: August 14, 2014
Additional Notes: This research was supported in part by NSERC
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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