Cusp Kähler–Ricci flow on compact Kähler manifolds

Abstract

In this paper, we study the limiting flow of conical Kahler–Ricci flows when the cone angles tend to 0. We prove the existence and uniqueness of this limiting flow with cusp singularity on compact Kahler manifold M which carries a smooth hypersurface D such that the twisted canonical bundle $$K_M+D$$ is ample. Furthermore, we prove that this limiting flow converge to a unique cusp Kahler–Einstein metric.