Inserted: 6 apr 2009
Last Updated: 16 feb 2015
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Starting from a mass transportation proof of the Brunn-Minkowski inequality on convex sets, we improve the inequality showing a sharp estimate about the stability property of optimal sets. This is based on a Poincaré-type trace inequality on convex sets that is also proved in sharp form.