The i th p -affine surface area

Journal of inequalities and applications

Tongyi Ma¹ 

关键词: convex bodies;    ith p-affine surface area;    ith p-affine area ratio;    Blaschke-Santaló inequality;    Brunn-Minkowski-Firey theory;    52A30;    52A40;   

DOI  :  10.1186/s13660-015-0703-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

About two decades ago Lutwak introduced the concept of p-affine surface area. More recently, the results of Lutwak have been generalized by Ma to the entire class of so-called ith p-affine surface areas. In this paper, we further research this new notion and give its integral representation. Affine isoperimetric and Blaschke-Santaló inequalities, which generalize the inequalities obtained by Lutwak, are established. Furthermore, we prove the ith p-affine area ratio of convex body K for the ith p-affine surface area, which does not exceed the generalized Santaló product of convex body K.

【 授权许可】

CC BY