| Inequalities relating to Lp-version of Petty＇s conjectured projection inequality |
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| 引用本文： | 王卫东,冷岗松.Inequalities relating to Lp-version of Petty＇s conjectured projection inequality[J].应用数学和力学(英文版),2007,28(2):269-276. |
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| 作者姓名： | 王卫东 冷岗松 |
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| 作者单位： | [1]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China; [2]Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei Province, P. R. China |
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| 基金项目： | 国家自然科学基金;湖北省教育厅重点自然科学研究基金 |
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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 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.
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| 关 键 词： | 不等式 多维空间几何 单一性 几何方程 |
| 收稿时间： | 2005-06-27 |
| 修稿时间： | 2006-11-30 |
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