Calculus of Variations and Geometric Measure Theory

A. Figalli - F. Maggi - A. Pratelli

A refined Brunn-Minkowski inequality for convex sets

created by maggi on 06 Apr 2009
modified by pratelli on 16 Feb 2015


Published Paper

Inserted: 6 apr 2009
Last Updated: 16 feb 2015

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2009


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.