Sharp quantitative stability of the planar Brunn-Minkowski inequality

Peter van Hintum, Hunter Spink, Marius Tiba

We prove a sharp stability result for the Brunn-Minkowski inequality for $A,B\subset {\mathbb{R}}^2$. Assuming that the Brunn-Minkowski deficit $δ=|A+B|^{\frac{1}{2}}/(|A|^\frac12+|B|…