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

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.