混合相交体的对偶Minkowski不等式的均质积分形式  

Dual Quermassintegral Version of Minkowski Inequality for Mixed Intersection Bodies

作　　者：刘顺保[1] 袁淑锋[2] 

机构地区：[1]湖南师范大学数学与计算机科学学院,湖南长沙410081 [2]绍兴文理学院上虞分院,浙江上虞312300

出　　处：《湖南文理学院学报（自然科学版）》2006年第4期6-8,29,共4页Journal of Hunan University of Arts and Science(Science and Technology)

摘　　要：混合相交体是对偶Brunn-Minkowski理论中的一个重要研究对象,由于混合相交体的概念出现较晚,对它的讨论与研究比较缺乏.对此,主要在对偶Brunn-Minkowski理论的指导下,建立了关于混合相交体的经典Minkowski不等式的对偶均质积分形式.Mixed intersection bodies is an importantly object in the dual Brunn-Minkowski theory. Since the notion of mixed intersection bodies is raised recently, their properties have not been studied in detail by now. In this paper, a dual quermassintegral version of classical Minkowski inequality from the dual Brunn-Minkowski Theory is developed for mixed intersection bodies： If K,L are star bodies containing the origin in their interiors, and 0 ≤ i 〈 n, 1 ≤ j ≤ n-1 ,then. Wi（Ij（K,L））^n-1 ≤Wi（IK）^n-j-1Wi（IL）^j, With equality if and only if K and L are dilates.

关 键 词：混合相交体 对偶Brunn-Minkowski理论 对偶均质积分 MINKOWSKI不等式 

分 类 号：O186.5[理学—数学]