On a twisted conical Kähler-Ricci flow

Abstract

In this paper, we discuss diameter bound and Gromov-Hausdorff convergence of a twisted conical Kähler-Ricci flow on the total spaces of some holomorphic submersions. We also observe that, starting from a model conical Kähler metric with possibly unbounded scalar curvature, the conical Kähler-Ricci flow will instantly have bounded scalar curvature for $t>0$, and the bound is of the form $\frac{C}{t}$. Several key results will be obtained by direct arguments on the conical equation without passing to a smooth approximation. In the last section, we present several remarks on a twisted Kähler-Ricci flow and its convergence.

V3, small changes; accepted by Annals of Global Analysis and Geometry

References in corpus (4)

• Bounding diameter of singular Kähler metric
• The local entropy along Ricci flow---Part A: the no-local-collapsing theorems
• The continuity method on Fano fibrations
• Smooth approximation of the modified conical Kähler-Ricci flow