# Pseudo-Calabi Flow - Mathematics > Differential Geometry

Abstract: We first define Pseudo-Calabi flow, as {equation*}{{aligned}{{\partial \varphi}\over {\partial t}}and= -f\varphi,\triangle varphi f\varphi and= S\varphi - \ul S.{aligned}. \end{equation*}Then we prove the well-posedness of this flow including the short timeexistence, the regularity of the solution and the continuous dependence on theinitial data. Next, we point out that the $L^\infty$ bound on Ricci curvatureis an obstruction to the extension of the pseudo-Calabi flow. Finally, we showthat if there is a cscK metric in its K\-ahler class, then for any initialpotential in a small $C^{2,\alpha}$ neighborhood of it, the pseudo-Calabi flowmust converge exponentially to a nearby cscK metric.

Author: Xiuxiong Chen, Kai Zheng

Source: https://arxiv.org/