We consider the Kähler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kähler manifold . Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in terms of cohomological data on . We also give a sufficient condition for the singularity, if there is one, to be type II.
John Lott. Zhou Zhang. "Ricci flow on quasi-projective manifolds." Duke Math. J. 156 (1) 87 - 123, 15 January 2011. https://doi.org/10.1215/00127094-2010-067