Affine diameters of convex bodies

Imre Barany, Daniel Hug, Rolf Schneider

Published 2014-03-27, updated 2014-05-07Version 2

We prove sharp inequalities for the average number of affine diameters through the points of a convex body $K$ in ${\mathbb R}^n$. These inequalities hold if $K$ is either a polytope or of dimension two. An example shows that the proof given in the latter case does not extend to higher dimensions.