凸体的对偶迷向常数与LYZ椭球

The Dual Isotropic Constant and the LYZ Ellipsoid of Convex Bodies

研究了凸体处于对偶迷向位置时的解析特征,并建立了凸体对偶迷向常数的新的下界;其次,证明了关于原点中心对称凸体的LYZ椭球与John椭球相等的充要条件;最后,举例具体计算了几个凸多边形的LYZ椭球和John椭球,以进一步认清两者的差别.

We mainly study the analytical characterizations of convex bodies when they are positioned in the dual isotropic position.Several new lower bounds are established for the dual isotropic constant.Also we find the necessary and sufficient conditions such that the LYZ ellipsoid and the John eUipsoid are the same.To further distinguish the two important ellipsoids,we calculate and depict the LYZ ellipsoids and John ellipsoids of several specific convex polygons.