Blow-up rate of the scalar curvature along the conical K\"ahler-Ricci flow with finite time singularities

Abstract

We investigate the scalar curvature behavior along the normalized conical K\"ahler-Ricci flow $\omega_t$, which is the conic version of the normalized K\"ahler-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.