ABSTRACT
N E W IN E Q U A L IT IE S F O R M IX E D V O L U M E S A N D T H E IR A P P L IC A T IO N S
Using the Brunn theorem, Minkowski demonstrated tha t the inequality
holds between the mixed volumes of two convex bodies. Basing on it, we prove a
T h eo rem . Let be convex bodies in Eucledian space o f dimension n and let Z be the difference o f some convex functions on the unit sphere,2 then
V {H U . ■ •, Z )2 > V (H U . . . , //„ _ !) V {H U . . . , Hn. 2, Z , Z).
