Covering functionals of cones and double cones.

Abstract

The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m), and it is denoted by ${\Gamma }_m\left(K\right)$ . Estimating covering functionals of convex bodies is an important part of Chuanming Zong's quantitative program for attacking Hadwiger's covering conjecture. Estimations of covering functionals of cones and double cones, which are best possible for certain pairs of m and K, are presented.