摘要
根据Lutwak引进的凸体i次宽度积分的概念,本文获得了凸体i次宽度积分的Blaschke-Santal幃不等式,并把Ky Fan不等式推广到了凸体i次宽度积分.最后,本文利用其与对偶均质积分之间的关系建立了两个中心对称凸体的极的Brunn-Minkowski型不等式.
Inequalities similar to the Blaschke-Santalo inequality for the i- th width-integrals of convex bodies established by Lutwak,are shown to exist,the Ky Fan inequalities are generalized to the i- th width-integrals of convex bodies. Using the relations between it and the dual quermass-integrals, the Brunn-Minkowski inequality for the polar of the centrally symmetric bodies are given.
出处
《应用数学》
CSCD
北大核心
2006年第3期632-636,共5页
Mathematica Applicata
基金
国家自然科学基金资助项目(10271071)
关键词
凸体
对偶均质积分
宽度积分
p-宽度
Convex body
Dual quermassintegrals
Width-integrals
p- width
