一些几何不等式的等价关系  

Equivalence properties of some geometric inequalities

作　　者：袁淑峰[1,2] 金海林[1] 

机构地区：[1]上海大学理学院,上海200444 [2]绍兴文理学院上虞分院,浙江上虞312300

出　　处：《上海大学学报（自然科学版）》2015年第6期725-731,共7页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11271244);浙江省教育厅科研基金资助项目(Y201328555)

摘　　要：Brunn-Minkowski不等式和Minkowski不等式是凸几何中的两个重要而基本的不等式.近期,已有学者得到了这两个不等式的Orlicz版本,从而构建起Orlicz-Brunn-Minkowski理论的框架.本工作证明经典的Brunn-Minkowski不等式、Minkowski不等式、Orlicz-BrunnMinkowski不等式和Orlicz-Minkowski不等式是等价的.Brunn-Minkowski inequality and Minkowski inequality are two important and fundamental inequalities in convex geometric analysis. Recently, some researchers established Orlicz extension of these two inequalities, and constructed a general framework for the Orlicz-Brunn-Minkowski theory. The purpose of this paper is to show equivalence properties of these four inequalities, i.e., classical Brunn-Minkowski inequality, classical Minkowski inequality, Orlicz-Brunn-Minkowski inequality and Orlicz-Minkowski inequality.

关 键 词：BRUNN-MINKOWSKI不等式 MINKOWSKI不等式 Minkowski和 Orlicz和 均质积分 

分 类 号：O186.5[理学—数学]