Buttazzo–Gavitońe conjecture on the sharp upper bound for normalized torsional rigidity

Let $n\geq 2$ and let $\mathcal{K}_n$ denote the class of convex bodies in $\mathbb{R}^n$. For a domain $\Omega\in\mathcal{K}_n$, let $T(\Omega)$ be its torsional rigidity, $P(\Omega)$ its perimeter, and $|\Omega|$ its volume, and define

$$\mathcal F(\Omega)=\frac{T(\Omega)P^2(\Omega)}{|\Omega|^3}.$$

Buttazzo–Gavitońe conjecture. The sharp upper bound for $\mathcal F$ in arbitrary dimension is

$$\sup\{\mathcal F(\Omega):\Omega\in\mathcal{K}_n\}=\frac{2n^2}{(n+1)(n+2)}.$$

The conjecture extends Makai's sharp planar upper bound to higher dimensions. Its status is not specified in the supplied text.