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.