Inequalities for convex bodies and their polar bodies

摘要

The infimum of the quermassintegral product W_i(K)W_i(K*) for i = n - 1 was established by Lutwak. In this paper, the infimum of the dual quermassintegral product W?_(n+p)(K)W?_(n+p)(K*) for any p ≥ 1 is obtained, and some new inequalities about convex bodies and their polar bodies are established.