This is an announcement for the paper "Interpolations, convexity and geometric inequalities" by Dario Cordero-Erausquin and Boaz Klartag.

Abstract: 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.

Archive classification: math.FA math.CV

Submitted from: cordero@math.jussieu.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1109.3652

or

http://arXiv.org/abs/1109.3652