Affine constructions and inequalities
The mixed volume V(K1, …, Kn), which is a central notion of the Brunn–Minkowski theory, remains unchanged if the same volume-preserving affine transformation of is applied to each of the convex bodies K1, …, Kn. The general theory of mixed volumes thus belongs to the affine geometry of convex bodies.
This affine geometry of convex bodies has much more to offer. In fact, affineinvariant constructions, functionals and extremum problems for convex bodies are a rich source of questions and results of considerable geometric beauty. Moreover, surprising relations to some other fields and unexpected applications ...