Mathematical Research Letters

Volume 14 (2007)

Number 6

The Calabi flow with small initial energy

Pages: 1033 – 1039



Valentino Tosatti (Harvard University)

Ben Weinkove (Harvard University)


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.

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