Uniqueness of the limiting cohomology class of conjugate p-tight forms

Let $M$ be a closed oriented Riemannian manifold of dimension $2\leq d\leq 7$. Let $\rho\in H^{d-1}(M,\mathbf{R})$ be nonzero, and for each $1<p<\infty$ let $F_p$ be the $p$-tight form representing $\rho$. Define

$$\alpha_q\in H^1(M,\mathbf{R})$$

to be the cohomology class of $|F_p|^{p-2}\star F_p$.

Uniqueness conjecture. The family $(\alpha_q)$ has a unique limit as $q\to1$. This asks whether the limiting cohomology class arising from the $q$-harmonic conjugates is distinguished among all classes dual to the given class; the paper presents it as an open question.