凸体的L_p John椭球与其L_p迷向性  

L_p John ellipsoids and isotropy of convex bodies

作　　者：贺汕森 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2016年第3期332-338,共7页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11001163);上海市教委科研创新基金资助项目(11YZ11)

摘　　要：利用凸体的L_p混合体积理论,证明了R^n中关于原点对称的凸体K的L_p迷向性等价于其L_p John椭球为球这一充要条件.作为应用,验证了R^n中单位立方体的L_p迷向性.最后,根据L_p John椭球的仿射不变性,证明了R^n中所有超平行体的L_p John椭球就是经典的John椭球.By using the theory of Lp mixed volumes, this paper mainly proves the equivalence between the Lp isotropy and that the Lp John ellipsoids are precisely balls. As an example, we verify the Lp isotropy of unit cubes in Rn. According to the affine invariant of Lp John ellipsoids, we prove all the Lp John ellipsoids of parallelotopes are identical to the classical John ellipsoids.

关 键 词：Lp混合体积 Lp迷向性 LP John椭球 LP 表面积测度 仿射不变性 

分 类 号：O186.5[理学—数学]