The Calabi flow on toric Fano surface

Abstract

We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian potential and the initial Calabi energy is bounded by some constant. This is an extension of our previous work. We use the toric condition in a more essential way to rule out bubbles.

Some errors are corrected and Section 3 is thoroughly rewritten

References in corpus (6)

• Interior estimates for solutions of Abreu's equation
• Extremal metrics on blow ups
• The Calabi flow on Kähler surface with bounded Sobolev constant
• Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance
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Cited by in corpus (6)

• 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
• Convergence of the calabi flow on toric varieties and related Kaehler manifolds
• On the Extension of the Calabi Flow on Toric Varieties
• On the extension and smoothing of the Calabi flow on complex tori