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

TL;DR

This paper studies the behavior of scalar curvature in the conical K"ahler-Ricci flow as it approaches finite-time singularities, establishing an upper bound that generalizes previous results to the conic setting.

Contribution

It extends the understanding of scalar curvature blow-up rates to the conical K"ahler-Ricci flow with finite-time singularities, generalizing prior work by Zhang.

Findings

Scalar curvature is bounded by C/(T-t)^2 near singularity

Generalization of Zhang's results to conic K"ahler-Ricci flow

Provides bounds under contraction associated with limiting cohomology class

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.