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Lp-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.
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.
出处
《应用数学和力学》
CSCD
北大核心
2007年第2期245-252,共8页
Applied Mathematics and Mechanics
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)
