Corollary 5.2 . [021D]

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Corollary 5.2.

For any $0<q<\infty$ , there exists a constant $C_{5.2}$ , depending only on the background metric $g$ , the choice of $\Phi$ , the bound $\int_{M}e^{F}\Phi(F)dvol_{g}$ , and $q$ , such that

(5.6)

\int_{M}e^{qF}dvol_{g}\leq C_{5.2},\textrm{ $||\varphi||_{0}\leq C_{5.2}$, $||\psi||_{0}\leq C_{5.2}.$}