The Modified Cusp Kähler–Ricci Flow and Soliton

Abstract

In this paper, we study the limiting flow of conical Kahler–Ricci flow modified by a holomorphic vector field on a compact Kahler manifold M which carries an effective $${\mathbb {R}}$$ -ample divisor D with simple normal crossing support. By smooth approximation, we prove the existence and uniqueness of the flow with cusp singularity when the twisted canonical bundle $$K_M+D$$ is ample. At last, we show that the flow converges to a soliton-type metric.