Inequalities relating to L_p-version of Petty's conjectured projection inequality  

作　　者：王卫东 冷岗松 

机构地区：[1]Department of Mathematics,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第2期269-276,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.10671117);the Key Science Research Foundation of Education Department of Hubei Province of China(No.2003A005).

摘　　要：Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.

关 键 词：Lp-version Petty projection inequality Petty＇s conjectured projectioninequality Lp-projection body REVERSE 

分 类 号：O178[理学—数学]