L_p-混合质心体和对偶L_p-混合质心体  

On L_p-Mixed Centroid Bodies and Dual L_p-Mixed Centroid Bodies

作　　者：马统一[1] 

机构地区：[1]河西学院数学系,张掖734000

出　　处：《数学学报（中文版）》2010年第2期301-314,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10971128);甘肃省教育厅科研资助项目(0709-03)

摘　　要：本文引进了L_p-混合质心体Γ_(p,i)K、对偶L_p-混合质心体Γ_(-p,i)K和R^n中星体K和L的L_p-混合调和Blaschke加K+_pL的概念,成功地解决了L_p-混合质心体和对偶L_p-混合质心体的Shephard型问题.并且结合星体的L_p-混合调和Blaschke加的概念,分别建立了L_p-混合质心体的均质积分和对偶均质积分的Brunn-Minkowski型不等式.所获结论推广了已有文献的结果.In this paper, the three concepts of Lp-mixed centroid bodies Гp,iK and dual Lp-mixed centroid bodies Гp,iK and Lp-mixed harmonic Blaschke add K ＋p L of star bodies K, L C R^n are introduced. The Shephard＇s question of Lp-mixed cen- troid bodies and dual Lp-mixed centroid bodies are solved succeed. In addition, the Brunn-Minkowski inequalities of the quermassintegrals and dual quermassintegrals of Lp-mixed centroid bodies associated with Lp-mixed harmonic Blaschke add are established, respectively. They extend some results of before document.

关 键 词：Lp-混合质心体 对偶Lp-混合质心体 均质积分 

分 类 号：O184[理学—数学]