Calabi flow on toric varieties with bounded Sobolev constant, I

Hongnian Huang

Let $(X,P)$ be a toric variety. In this note, we show that the $C^0$-norm of the Calabi flow $\phi (t)$ on $X$ is uniformly bounded in $[0,T)$ if the Sobolev constant of $\phi (t)$ is un…