凸体覆盖泛函的估计与关于凸体覆盖的Hadwiger猜想

Estimations of covering functionals of convex bodiesand Hadwiger's covering conjecture

凸体覆盖泛函的估值是凸几何和离散几何中的一个自然、基本且有难度的研究问题。该文回顾了凸体覆盖泛函的定义,阐明凸体覆盖泛函的估计与关于凸体覆盖的Hadwiger猜想之间的关系,介绍了基于凸体覆盖泛函估计的用以攻克Hadwiger猜想不等式部分的方案,综述了有关凸体覆盖泛函估计的现有结果。

Estimating covering functionals of convex bodies is a natural,fundamental,and difficult problem from convex and discrete geometry.The definitions of covering functionals are reviewed,the relation between estimations of covering functionals and Hadwiger's covering problem are clarified,the program to attack the inequality part of Hadwiger's covering conjecture which is based on estimations of covering functionals is presented,and the known results on estimations of covering functionals are surveyed.