On the convergence of the Calabi flow

He, Weiyong

doi:10.1090/S0002-9939-2014-12318-5

On the convergence of the Calabi flow
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Proc. Amer. Math. Soc. 143 (2015), 1273-1281 Request permission

Abstract:

Let $(M, [\omega _0], J)$ be a compact Kähler manifold without holomorphic vector field. Suppose $\omega _0$ is (the unique) constant scalar curvature metric. We show that the Calabi flow with any smooth initial metric converges to the constant scalar curvature metric $\omega _0$ with the assumption that Ricci curvature stays uniformly bounded.

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