The global existence and convergence of the Calabi flow on ${\mathbb{C}}^n/{\mathbb{Z}}^n+i{\mathbb{Z}}^n$

Renjie Feng, Hongnian Huang

In this note, we study the long time existence of the Calabi flow on $X={\mathbb{C}}^n/{\mathbb{Z}}^n+i{\mathbb{Z}}^n$. Assuming the uniform bound of the total energy, we establish t…