UPPER BOUNDS FOR THE COVERING NUMBER OF CENTRALLY SYMMETRIC CONVEX BODIES IN R-n

作者：Wu, Senlin^*

来源：Mathematical Inequalities & Applications, 2014, 17(4): 1281-1298.

DOI：10.7153/mia-17-93

• Banach-Mazur distance
• Birkhoff orthogonality
• blocking number
• covering number
• generalized blocking number
• Hadwiger's covering conjecture
• radial projection of bisector
• shadow boundary

The covering number c(K) of a convex body K is the least number of smaller homothetic copies of K needed to cover K. We provide new upper bounds for c(K) when K is centrally symmetric by introducing and studying the generalized alpha-blocking number beta(alpha)(2)(K) of K. It is shown that when a centrally symmetric convex body K is sufficiently close to a centrally symmetric convex body K', then c(K) is bounded by beta(alpha)(2)(K') from above, where alpha is a properly chosen number. Related results in Minkowski geometry are also presented.

• 出版日期2014-10
• 单位哈尔滨学院