Bulletin of the
Korean Mathematical Society BKMS

In this paper, we obtain some geometric inequalities for mixed volumes of a convex body and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual.

Keywords: convex body, centrally symmetric convex body, mixed volume, dual mixed volume, polar dual, radial function, support function

MSC numbers: 52A40, 52A20, 53A15