Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow

Abstract

We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-W₁ distances. In particular, the singular sets of each time slice and its tangent cones are closed and of codimension no less than 4.