Affine diameters of convex bodies
  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. 
Imre Barany, Daniel Hug, Rolf Schneider
math.MG