Lemma 3.30 . [043X]

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Lemma 3.30.

The volume form error for $\tilde{g}^{(4)}$ admits bound in $\{|\vec{\mu}|_{a}\leq\frac{1}{3}A^{1/2}\}$ :

\tilde{E}^{(4)}=\frac{4}{3}\frac{(\tilde{\omega}^{(4)})^{3}}{\sqrt{-1}\Omega\wedge\overline{\Omega}}-1,\quad\left\lVert\tilde{E}^{(4)}\right\rVert_{C^{k,\alpha}_{-1-\epsilon,0}(\mathbb{C}^{3}\cap\{|\vec{\mu}|_{a}\leq\frac{1}{3}A^{1/2}\})}\leq C\nu^{2}A^{3/4(-1+\epsilon)}.