## Duke Mathematical Journal

### 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 $\overline{X}$. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in terms of cohomological data on $\overline{X}$. We also give a sufficient condition for the singularity, if there is one, to be type II.

#### Article information

Source
Duke Math. J., Volume 156, Number 1 (2011), 87-123.

Dates
First available in Project Euclid: 16 December 2010

https://projecteuclid.org/euclid.dmj/1292509119

Digital Object Identifier
doi:10.1215/00127094-2010-067

Mathematical Reviews number (MathSciNet)
MR2746389

Zentralblatt MATH identifier
1248.53050

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 32Q15: Kähler manifolds

#### Citation

Lott, John; Zhang, Zhou. Ricci flow on quasi-projective manifolds. Duke Math. J. 156 (2011), no. 1, 87--123. doi:10.1215/00127094-2010-067. https://projecteuclid.org/euclid.dmj/1292509119

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