Ricci flow on quasi-projective manifolds

Abstract

We consider the Kähler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kähler manifold $\stackrel{̲}{X}$. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in terms of cohomological data on $\stackrel{̲}{X}$. We also give a sufficient condition for the singularity, if there is one, to be type II.