内平行体的均质积分  

The i-th quermassintegral of inner parallel bodies

作　　者：朱保成[1] 徐文学[2] 

机构地区：[1]湖北民族学院数学系,恩施445000 [2]西南大学数学与统计学院,重庆400715

出　　处：《中国科学：数学》2016年第6期807-816,共10页Scientia Sinica：Mathematica

基　　金：湖北民族学院博士启动基金(批准号:MY2014B001);国家自然科学基金(批准号:11401486)资助项目

摘　　要：由于凸集的内平行体的边界结构非常复杂,难以控制,而且它的体积等测度在一般情况下无法计算.因此,Matheron等考虑利用原来凸体的相关量来刻画内平行体体积.本文研究了第i阶均质积分的Matheron猜想,证明了凸集的内平行体的均质积分的有界性,并给出了内平行体的均质积分的上界和下界.利用所得到的一个结果分析了Matheron猜想是不成立的.Because of the boundary structure of the inner parallel body of a convex set is very complicated and difficult to control, moreover, its volume and other measures cannot be computed in the general case. Therefore,Matheron and others considered to use the information of the original convex body to describe the volume of inner parallel body. In this paper a conjecture of Matheron for i-th quermassintegral is studied. We provide bounds for the quermassintegrals of inner parallel body of a convex set. As a result, we show that the non-validity of Matheron＇s conjecture.

关 键 词：均质积分 内平行体 核 凸体 

分 类 号：O186.5[理学—数学]