Theorem 5.2 . [021C]

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Theorem 5.2.

Given any $0<\varepsilon<1$ , there exists a constant $C_{5.1}$ , depending on $\varepsilon$ , the background metric $g$ , the choice of $\Phi$ , and the bound $\int_{M}e^{F}\Phi(F)dvol_{g}$ , such that

(5.5)

F+\varepsilon\psi-2(1+\max_{M}|Ric|)\varphi\leq C_{5.1}.