Sharp quantitative stability of the Brunn-Minkowski inequality

Alessio Figalli, Peter van Hintum, Marius Tiba

The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in ${\mathbb{R}}^n$, we have $|A+B{|}^{1/n}\ge |A{|}^{1/n}+|B{|}^{1/n}$. Also, equality holds if and on…