关于凸体覆盖的Hadwiger猜想  

Hadwiger's Covering Conjecture

作　　者：吴森林[1] 王丹[1] 庞海婧 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2014年第1期117-123,共7页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11371114;11171082)

摘　　要：针对Hadwiger猜想这一凸和离散几何中持续了近60年的著名难题,回顾了这一猜想的提出,它的若干等价形式,以及前人在尝试解决这一猜想的过程中取得的阶段性进展.介绍了该猜想相关的若干研究问题及相应结果.结果表明:一方面,Hadwiger猜想仍是一个远未解决的公开难题;另一方面,围绕着Hadwiger猜想及其相关问题还有大量亟待完成的基础性研究工作。Abstract：The origin, equivalent forms, and existing partial results concerning Hadwiger＇ s covering conjec- ture, which is a famous open problem that has lasted for nearly 60 years from convex and discrete geometry, are re- viewed. Related research problems and corresponding results are also presented. It is shown that, on the one hand, Hadwiger＇ s conjecture is still a very hard open problem, and, on the other hand, there are a lot of fundamental re- searches to be done concerning this conjecture and problems related to it.

关 键 词：Hadwiger猜想 凸体 位似体 等宽体 

分 类 号：O177[理学—数学]