Dual higher-order Bol inequality for normal solutions with lower-bounded Q-curvature

Let $n\geq 2$ be an even integer, and let $u$ be a normal solution on $\mathbb{R}^n$ of

$$(-\Delta)^{\frac{n}{2}}u=Qe^{nu}$$

with $Q(x)\geq (n-1)!$.

Dual higher-order Bol inequality conjecture. One should have

$$\int_{\mathbb{R}^n}e^{nu}\\,\mathrm{d}x\leq |\mathbb{S}^n|,$$

with equality if and only if $Q(x)\equiv(n-1)!$.

This is presented as the dual version of the upper-bound conjecture. Unlike the special cases established for the first conjecture, no corresponding general resolution is supplied here, so the dual assertion remains open.