A quantitative program for Hadwiger's covering conjecture

作     者：ZONG Chuanming School of Mathematical Sciences,Peking University,Beijing 100871,China 

作者机构：School of Mathematical Sciences Peking University Beijing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第9期

页      面：2551-2560页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.10225104) the Chang Jiang Scholars Program and LMAM at Peking University 

主　　题：convex body Hadwiger’s conjecture Banach-Mazur metric β-net Borsuk’s conjecture 

摘      要：In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its *** to now,this conjecture is still open for all n *** 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller *** to now,this conjecture is open for 4 n *** this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.