The Covering Number, Blocking Number and
Kissing Number of a Convex Body

Chuanming Zong
Peking University,
Beijing 100000,
P.R.China

Abstract    
LetC be ann-dimensional convex body, especially let Bⁿ denote an n-dimensional unit ball. The covering number h(C) ofC is the smallest number of translates of int (C) such that their union can cover C; the blocking number b(C) of C is the smallest number of the non-overlapping translates of C, all of them touch C, that can block any other translate from touching C; the kissing number k(C) of C is the maximal number of non-overlapping translates of C which can touch C. In 1694, Newton proposed the problem to determine k(B³). In 1957, Hadwiger made a conjecture that h(C) 2ⁿ. This talk will review some main results and some key problems about these three numbers. Especially, we will show some connections between them.