On the Hölder Estimate of Kähler–Ricci Flow.

It is conjectured by Song–Tian that the normalized Kähler–Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle is uniformly smooth away from the singular fibers. In this work, we adapt the method in the work of Hein–Tosatti on collapsing Calabi–Yau metrics and obtain a uniform spatial Hölder estimate along the normalized Kähler–Ricci flow for all time away from the singular fiber. [ABSTRACT FROM AUTHOR]