Mathematical Research Letters

Volume 14 (2007)

Number 6

The Calabi flow with small initial energy

Pages: 1033 – 1039

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

Authors

Valentino Tosatti (Harvard University)

Ben Weinkove (Harvard University)

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.

Published 1 January 2007