Extremal mean width when covering the 1-skeleton
Abstract
For a given convex body K in ℝ d , let D n be the compact convex set of maximal mean width whose 1-skeleton can be covered by n congruent copies of K . Based on the fact that the mean width is proportional to the average perimeter of two-dimensional projections, it is proved that D n is close to being a segment for large n .