The pseudo-Calabi flow

We define the pseudo-Calabi flow as [equation presented] Then we prove the well-posedness of this flow including the short time existence, the regularity of the solution and the continuous dependence on the initial data. Next, we point out that the L^∞ bound on Ricci curvature is an obstruction to the extension of the pseudo-Calabi flow. Finally, we show that if there is a constant scalar curvature Kähler metric o in its Kähler class, then for any initial potential in a small C^2,α neighborhood of this metric (defined in terms of the C^2,α norm on the Kähler potential), the pseudo-Calabi flow must converge exponentially fast to a constant scalar curvature Kähler metric near o within the same Kähler class.