Non-intersection bodies, all of whose central sections are intersection bodies

Yaskina, M.

doi:10.1090/S0002-9939-06-08530-3

Non-intersection bodies, all of whose central sections are intersection bodies
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Proc. Amer. Math. Soc. 135 (2007), 851-860 Request permission

Abstract:

We construct symmetric convex bodies that are not intersection bodies, but all of their central hyperplane sections are intersection bodies. This result extends the studies by Weil in the case of zonoids and by Neyman in the case of subspaces of $L_p$.

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