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联系投影不等式Petty猜想的Lp-形式的不等式
  • ISSN号：1000-0887
  • 期刊名称：《应用数学和力学》
  • 时间：0
  • 分类：O184[理学—数学;理学—基础数学]
  • 作者机构：[1]上海大学数学系,上海200436, [2]湖北民族学院数学系,湖北恩施445000
  • 相关基金：国家自然科学基金资助项目（10671117）;湖北省教育厅重点科研项目（2003A005）王卫东（1959-）,男,湖北巴东人,教授,博士（联系人.Tel：＋86-718-8960711;Fax：＋86-718-8437732;E-mail：wdwxh722@163.com）.
作者： 王卫东[1,2], 冷岗松[1]
关键词： Lp-形式, Petty投影不等式, 投影不等式的Petty猜想, Lp-投影体, 逆向不等式, Lp-version, Petty projection inequality, Petty＇s conjectured projection inequality, Lp-projection body, reverse
中文摘要：

在凸体理论中，投影不等式的Petty猜想是一个著名的公开问题．首先通过利用Lp-混合体积和分对偶混合体积的概念、Lp-投影体和几何体Γ-pK的关系、Bourgain-Milman不等式和Lp-Busemann—Petty不等式，建立了一个联系投影不等式Petty猜想的Lp-形式的不等式．继而对于每一个关于原点对称的凸体，应用Jensen不等式和几何体Γ-pK的单调性，分别给出了投影不等式Petty猜想的Lp-形式的一个逆向不等式和Lp-Petty投影不等式的一个逆向不等式．

英文摘要：

Petty＇s conjectured projection inequality is a famous open problem in convex bodies theory. It was shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality 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 Γ-pK, the Bourgain-Milman inequality and the Lp-Busemann-Petty inequality. In addition, for each origin-symmetzic convex body, applying the Jensen inequality and the monotonicity of the geometric body Γ-pK, the reverses of Lp-version of the Petty＇s projection inequality and the Lp-Petty projection inequality were given respectively.

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期刊信息
  • 《应用数学和力学》
  • 中国科技核心期刊
  • 主管单位:重庆交通大学
  • 主办单位:重庆交通大学
  • 主编：钟万勰
  • 地址：重庆南岸区重庆交通大学90信箱
  • 邮编：400074
  • 邮箱：applmathmech@cqjtu.edu.cn
  • 电话：023-62652450
  • 国际标准刊号：ISSN：1000-0887
  • 国内统一刊号：ISSN：50-1060/O3
  • 邮发代号:78-21
  • 获奖情况:
  • 国际工程索引（EI）收录期刊,我国力学类核心期刊,中国期刊方阵“双效”期刊
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  • 被引量:8965