Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation

Alessio Figalli, Peter van Hintum, Marius Tiba

The Brunn-Minkowski inequality, applicable to bounded measurable sets $A$ and $B$ in ${\mathbb{R}}^d$, states that $|A+B{|}^{1/d}\ge |A{|}^{1/d}+|B{|}^{1/d}$. Equality is achieved if and…