On the H\"older estimate of K\"ahler-Ricci flow

TL;DR

This paper establishes uniform H"older regularity estimates for the K"ahler-Ricci flow on compact K"ahler manifolds with semi-ample canonical bundle, extending understanding of its long-term behavior.

Contribution

It adapts Hein-Tosatti's method to prove uniform spatial H"older estimates for the K"ahler-Ricci flow on certain manifolds, a novel extension in the field.

Findings

Uniform spatial H"older estimate for all time

Extension of Hein-Tosatti's method to K"ahler-Ricci flow

Enhanced understanding of flow regularity on semi-ample manifolds

Abstract

In this work, we study the H\"older regularity of the K\"ahler- Ricci flow on compact K\"ahler manifolds with semi-ample canonical line bundle. By adapting the method in the work of Hein-Tosatti on collapsing Calabi-Yau metrics, we obtain a uniform spatial H\"older estimate of the K\"ahler-Ricci flow for all time.