1. CJM 2008 (vol 60 pp. 3)
|Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells |
Given $r>1$, we consider convex bodies in $\E^n$ which contain a fixed unit ball, and whose extreme points are of distance at least $r$ from the centre of the unit ball, and we investigate how well these convex bodies approximate the unit ball in terms of volume, surface area and mean width. As $r$ tends to one, we prove asymptotic formulae for the error of the approximation, and provide good estimates on the involved constants depending on the dimension.