Given a local 3-form $v$ defined on a neighborhood $\mathcal{U}$ of $p$ in $Q$ with $v=O^{\prime}(1)$, then there is some smaller neighborhood $\mathcal{V}\subset\subset\mathcal{U}$ such that there exists a local solution $T$ to the equation

(3.210)

$$\Delta T=v,$$

with $T=O^{\prime}(r^{2})$. Here $r$ is the distance to the submanifold $P$.