On the extension and smoothing of the Calabi flow on complex tori

Abstract

In this paper, we continue to study the Calabi flow on complex tori. We develop a new method to obtain an explicit bound of the curvature of the Calabi flow. As an application, we show that when $n=2$, the Calabi flow starting from a weak Kähler metric will become smooth immediately. It implies that in our settings, the weak minimizer of the Mabuchi energy is a smooth one.

References in corpus (8)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
• Interior estimates for solutions of Abreu's equation
• Space of Kähler metrics (IV)--On the lower bound of the K-energy
• The Calabi flow on Kähler surface with bounded Sobolev constant
• The Calabi flow on toric Fano surface
• On the Extension of the Calabi Flow on Toric Varieties