Duality of Floating and Illumination Bodies

We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question for the class of centrally symmetric convex bodies. We provid...

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Bibliographic Details
Published in:Indiana University mathematics journal 2020-01, Vol.69 (5), p.1507-1541
Main Authors: Mordhorst, Olaf, Werner, Elisabeth M.
Format: Article
Language:English
Online Access:Get full text
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Summary:We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question for the class of centrally symmetric convex bodies. We provide precise estimates for B p n and for centrally symmetric convex bodies with everywhere positive Gauss curvature. Our estimates show that equality of the polar of the floating body and the illumination body of the polar can only be achieved in the case of ellipsoids.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2020.69.7973