Theorem 5.1 . [021A]

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Theorem 5.1.

Let $(\varphi,F)$ be a smooth solution to cscK, then $\int_{M}e^{F}Fdvol_{g}$ can be bounded in terms of $||\varphi||_{0}$ . Conversely, a bound for $\int_{M}e^{F}Fdvol_{g}$ implies a bound for $||F||_{0}$ , in particular $||\varphi||_{0}$ .