Limit behavior of the twisted conical K\"ahler-Ricci flow with change in the cone angle

TL;DR

This paper investigates how the conical K"ahler-Ricci flow behaves as the cone angle approaches zero, showing convergence to a smooth flow with cusp singularities along the divisor.

Contribution

It establishes the limit behavior of the conical K"ahler-Ricci flow as the cone angle diminishes, revealing convergence to a flow with cusp singularities.

Findings

Flow converges to a smooth K"ahler-Ricci flow outside the divisor

Flow admits cusp singularity along the divisor

Convergence is unique as cone angle tends to zero

Abstract

In this paper, we study the limit behavior of the conical K\"ahler-Ricci flow as its cone angle tends to zero. More precisely, we prove that as the cone angle tends to zero, the conical K\"ahler-Ricci flow converges to a unique K\"ahler-Ricci flow, which is smooth outside the divisor and admits cusp singularity along the divisor.