Mathematical Research Letters

Volume 14, Issue 6, November 2007 pp. 1033-1039.

The Calabi flow with small initial energy

Authors: Valentino Tosatti (1) and Ben Weinkove (2)
Author institution: Harvard University (1) and Harvard University (2)

Summary: We show that on K\"ahler 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 K\"ahler class is close to the canonical class.

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