| Inequalities relating to L_p-version of Petty's conjectured projection inequality |
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| 作者姓名： | 王卫东 冷岗松 |
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| 作者单位： | Department of Mathematics Shanghai University，Department of Mathematics，Shanghai University，Shanghai 200444，P.R.China Department of Mathematics，Hubei Institute for Nationalities，Enshi 445000，Hubei Province，P.R.China，Shanghai 200444，P.R.China |
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| 基金项目： | 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). |
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| 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 L_p-version of the Petty's conjectured projection inequality is developed by using the notions of the L_p-mixed volume and the L_p-dual mixed volume,the relation of the L_p-projection body and the geometric bodyΓ_(-p)K,the Bourgain-Milman inequality and the L_p-Busemann- Petty inequality.In addition,for each origin-symmetric convex body,by applying the Jeusen inequality and the monotonicity of the geometric bodyΓ_(-p)K,the reverses of L_p-version of the Perry's conjectured projection inequality and the L_p-Petty projection inequality are given,respectively.
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Inequalities relating to L_p-version of Petty's conjectured projection inequality |
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| WANG Wei-dong LENG Gang-song.Inequalities relating to L_p-version of Petty's conjectured projection inequality[J].Applied Mathematics and Mechanics(English Edition),2007(2). |
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| Authors: | WANG Wei-dong LENG Gang-song |
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| Abstract: | |
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| Keywords: | L_p-version Petty projection inequality Petty's conjectured projection inequality L_p-projection body reverse |
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