Counterexamples to convexity of 𝑘-intersection bodies

Yaskin, Vladyslav

doi:10.1090/S0002-9939-2014-12254-4

Counterexamples to convexity of $k$-intersection bodies
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Proc. Amer. Math. Soc. 142 (2014), 4355-4363 Request permission

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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