The isotropic position and the reverse Santal\'{o} inequality
  We present proofs of the reverse Santal\'{o} inequality, the existence of M-ellipsoids and the reverse Brunn-Minkowski inequality, using purely convex geometric tools. Our approach is based on properties of the isotropic position. 
Apostolos Giannopoulos, Grigoris Paouris, Beatrice-Helen Vritsiou
math.MG