The Calabi flow with small initial energy

Abstract

We show that on Kahler 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 Kahler class is close to the canonical class.

7 pages

References in corpus (1)

• Unstable products of smooth curves

Cited by in corpus (7)

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• Stability of Calabi flow near an extremal metric
• The global existence and convergence of the Calabi flow on ${\mathbb{C}}^n/{\mathbb{Z}}^n+i{\mathbb{Z}}^n$
• Pseudo-Calabi Flow
• Kähler non-collapsing, eigenvalues and the Calabi flow