It is a direct consequence of the Brunn-Minkowski inequality that
\begin{equation} |A\oplus B| - \Big(\sqrt{|A|}+\sqrt{|B|}\Big)^2 \geq |A\oplus\tilde{B}| - \Big(\sqrt{|A|}+\sqrt{|\tilde{B}|}\Big)^2, \end{equation}
where $A,B,\tilde{B}\subset\mathbb{R}^2$ are convex and $\tilde{B}$ is homothetic to $A$, and $\oplus$ denotes the Minkowski addition.
Is it also true that
\begin{equation} |A\oplus B \oplus C| - \Big(\sqrt{|A|}+\sqrt{|B|}+\sqrt{|C|}\Big)^2 \geq |A\oplus B \oplus \tilde{C}| - \Big(\sqrt{|A|}+\sqrt{|B|}+\sqrt{|\tilde{C}|}\Big)^2, \end{equation}
where $A,B,C,\tilde{C}\subset\mathbb{R}^2$ are convex and $\tilde{C}$ is homothetic to $A \oplus B$ ?
