Lp-dual Quermassintegral sums  

作　　者：Chang-jian ZHAO Department of Information and Mathematics Sciences,College of Science,China Jiliang University,Hangzhou 310018,China 

出　　处：《Science China Mathematics》2007年第9期1347-1360,共14页中国科学：数学（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant No.10271071);Zhejiang Provincial Natural Science Foundation of China (Grant No.Y605065);Foundation of the Education Department of Zhejiang Province of China (Grant No.20050392)

摘　　要：In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.In this paper, we first introduce a concept of L p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results.

关 键 词：mixed volumes mixed projection bodies dual Quermassintegral sum polar of mixed projection bodies 52A40 53A15 

分 类 号：O186.5[理学—数学]