L_p-混合仿射表面积的不等式  

Some Inequalities for L_p-Mixed Affine Surface Area

作　　者：朱先阳[1] 

机构地区：[1]井冈山大学数学系,吉安343009

出　　处：《数学学报（中文版）》2013年第2期279-288,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11161024);江西省自然科学基金资助项目(2010GZC0115)

摘　　要：引入了第i个Lp-混合仿射表面积和Lp-极曲率像概念,建立了几个与新概念及Lp-质心体、p-Blaschke体有关的不等式,获得了关于Lp-混合仿射表面积的Blaschke-Santalo类不等式.所获结果能得到经典对偶Urysohn不等式的广义形式.In this paper, the concepts of the i th Lp-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lp-centroid bodies and p-Blaschke bodies are established. Moreover, a Blaschke-Santal6 type inequality for Lp-mixed affine surface area is established. Our results also imply a generalization of the class dual Urysohn inequalities.

关 键 词：Lp-混合仿射表面积 Lp-极曲率像 p-Blaschke线性组合 Lp-质心体 

分 类 号：O184[理学—数学]