Scalar Curvature Behavior for Finite Time Singularity of K\"ahler-Ricci Flow

TL;DR

This paper demonstrates that scalar curvature tends to blow up at finite time singularities in K"ahler-Ricci flows on closed manifolds, with some control under mild assumptions.

Contribution

It establishes the blow-up behavior of scalar curvature at finite time singularities in K"ahler-Ricci flows, providing conditions for controlling this blow-up.

Findings

Scalar curvature blows up at finite time singularities.

Control of the blow-up is possible under mild assumptions.

The results apply to closed manifolds in K"ahler-Ricci flow.

Abstract

In this short paper, we show that K\"ahler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.