  We prove a quantitative stability result for the Brunn-Minkowski inequality:
if $|A|=|B|=1$, $t \in [\tau,1-\tau]$ with $\tau>0$, and $|tA+(1-t)B|^{1/n}\leq
1+\delta$ for some small $\delta$, then, up to a translation, both $A$ and $B$
are quantitatively close (in terms of $\delta$) to a convex set $K$.
