一类特殊凸体的照亮与覆盖

Illumination Problem of a Special Class of Convex Bodie

鉴于凸体边界的照亮问题与凸体覆盖的Hadwiger猜想之间的密切联系,通过研究三维空间中一类特殊凸体的照亮问题,给出了其覆盖数的上界,并且验证了该类凸体在某些情况下Hadwiger猜想不等式部分的正确性.

In view of the close relation between the illumination problem of the boundary of a convex body and Hadwiger′s covering conjecture of convex bodies,the upper bound of the covering number of convex bodies is given by studying the illumination problem of a special class of convex bodies in 3-dimensional spaces,and the correctness of the inequality part of Hadwiger′s conjecture is verified in some cases.