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# Mathematical Research Letters

## Volume 14 (2007)

### Number 6

### The Calabi flow with small initial energy

Pages: 1033 – 1039

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n6.a11

#### Authors

#### Abstract

We show that on Kähler manifolds $M$ with $c_1(M)=0$ the Calabi flow converges to a constant scalar curvature metric if the initial Calabi energy is sufficiently small. We prove a similar result on manifolds with $c_1(M)<0$ if the Kähler class is close to the canonical class.