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A refined Brunn–Minkowski inequality for convex sets

Alessio Figalli, Francesco Maggi, Aldo Pratelli

Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2009 · 89 citations · 13 references

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Abstract

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.

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