Theorem 1.4 . [020J]

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Theorem 1.4.

(Corollary 5.4)Let $\varphi$ be a smooth solution to (1.1), (1.2), then there exists a constant $C$ , depending only on the background metric $(M,g)$ and an upper bound for $\int_{M}e^{F}Fdvol_{g}$ , such that

(1.4)

e^{F}\leq C.