Second-order estimates for collapsed limits of Ricci-flat Kähler metrics

Abstract

The purpose of this manuscript is to prove the conjectures made in [66,67] for maximally varying families of Calabi-Yau manifolds. In particular, these results confirm the conjectural understanding of collapsed Gromov-Hausdorff limits which arise in the study of the long-time behavior of the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical bundle and intermediate Kodaira dimension.