Duality, volume product and Mahler's inequalities
This is an invitation, on an educational level, to the geometry related to an important affine invariant of convex bodies, the volume product. After an introduction to duality in real vector spaces, the proof of Kurt Mahler's sharp lower bounds for the volume product of two-dimensional convex bodies, with or without center of symmetry, is presented in a neat way. The note concludes with a discussion of results and open problems on the volume product in higher dimensions.
scientific article; zbMATH DE number 5360655