With notation as in Proposition 3.5, let $R(\epsilon)$ denote the curvature tensor of the total space $X^{\prime}$ of the elliptic fibration over $D^{\prime}$, under an Ooguri–Vafa metric on $X^{\prime}$ with fibre volume $\epsilon$. Then there exists positive constants $C_{4},C^{\prime}_{4}$ (independent of $\epsilon$) such that, for all sufficiently small $\epsilon$,

$$C^{\prime}_{4}\epsilon^{-1}\log(\epsilon^{-1})^{-2}<\|R(\epsilon)\|_{C^{0}}<C_{4}\epsilon^{-1}\log(\epsilon^{-1}),$$

where $\|\ .\ \|_{C^{0}}$ denotes the usual $C^{0}$-norm on $X^{\prime}$.