Covering functionals of cones and double cones

Journal of Inequalities and Applications

Senlin Wu¹  Ke Xu¹ 

[1] Department of Applied Mathematics, Harbin University of Science and Technology;

关键词: Banach–Mazur distance;    Compact convex cones;    Convex body;    Covering;    Hadwiger’s covering conjecture;   

DOI  :  10.1186/s13660-018-1785-9

来源: DOAJ

【 摘 要 】

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 Γm(K) $\Gamma_{m}(K)$. 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.

【 授权许可】

Unknown