ScalingStacks

Theorem 4.6. [51, Thm. 1.4] (Uniform $L^{\infty}$-estimate) Given a large complex structure limit of Calabi-Yau manifolds, the potential of the Calabi-Yau metrics $\omega_{CY,t}$ in the class $\frac{1}{|\log|t||}c_{1}(L)$ relative to a fixed Fubini-Study reference metrics $\omega_{FS,t}$, have uniform $L^{\infty}$-estimate independent of $0<|t|\ll 1$, under suitable additive normalization.