Publication date:
9 July 2017
Source:Advances in Mathematics, Volume 314
Author(s): Alessio Figalli, David Jerison
We prove a quantitative stability result for the Brunn–Minkowski inequality: if $|A|=|B|=1$, $t\in [\tau ,1-\tau ]$ with $\tau >0$, and $|tA+(1-t)B{|}^{1/n}\le 1+\delta$ for some small δ, then, up to a translation, both A and B are quantitatively close (in terms of δ) to a convex set $\mathcal{K}$.