Blow-up rate of the scalar curvature along the conical Kähler-Ricci flow with finite time singularities

Abstract

We investigate the scalar curvature behavior along the normalized conical Kähler-Ricci flow ${\omega }_t$, which is the conic version of the normalized Kähler-Ricci flow, with finite maximal existence time $T<\infty$. We prove that the scalar curvature of ${\omega }_t$ is bounded from above by $C/(T-t{)}^2$ under the existence of a contraction associated to the limiting cohomology class $[{\omega }_T]$. This generalizes Z. Zhang's work to the conic case.

16pages, minor changes