Interpolations, convexity and geometric inequalities
  We survey some interplays between spectral estimates of H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o or Busemann inequalities. 
Dario Cordero-Erausquin and Bo'az Klartag
math.FA math.CV