Counterexamples to convexity of k-intersection bodies

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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2014-12, Vol.142 (12), p.4355-4363
Main Author: YASKIN, VLADYSLAV
Format: Article
Language:English
Subjects:
Continuous functions
Convexity
Curvature
Ellipsoids
Fourier transformations
Geometry
Integers
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2014-12254-4