Novaga–Ruffini conjecture on the Brunn–Minkowski inequality for Riesz capacity

Let $n\geq1$ and let $p\in(n-2,n)$. For compact sets $A,B\subset\mathbb R^n$ and $\lambda\in[0,1]$, write

$$\lambda A+(1-\lambda)B=\{\lambda a+(1-\lambda)b:a\in A,\ b\in B\}.$$

Let $\operatorname{Cap}_p$ denote the Riesz $p$-capacity. Novaga–Ruffini conjecture. The Brunn–Minkowski capacity inequality referred to in the source as Theorem $\operatorname{capBM}$ continues to hold for every $p\in(n-2,n)$.

The source explains that the inequality is known for several values, including $p=n-2$ and $p=n-1$, but leaves the interval $(n-2,n)$ as conjectural.