The Generalized L_p-Mixed Affine Surface Area  

作　　者：Tong Yi MA 

机构地区：[1]College of Mathematics and Statistics, Hexi University

出　　处：《Acta Mathematica Sinica,English Series》2015年第11期1775-1788,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11161019 and 11371224);the Science and Technology Plan of the Gansu Province(Grant No.145RJZG227)

摘　　要：Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.

关 键 词：Convex body star body i-th Lp-mixed curvature function i-th Lp-mixed curvature im-age （i j）-type Lp-mixed affine surface area 

分 类 号：O186.5[理学—数学]