Floating and Illumination Bodies for Polytopes: Duality Results

Abstract

We consider the question how well a floating body can be approximated by the polar of the illumination body of the polar. We establish precise convergence results in the case of centrally symmetric polytopes. This leads to a new affine invariant which is related to the cone measure of the polytope.

arXiv admin note: text overlap with arXiv:1709.02424

References in corpus (1)

• Relative entropy of cone measures and $L_p$ centroid bodies

Cited by in corpus (1)

• The Loewner function of a log-concave function