ScalingStacks

Theorem 5.2 . [021C]

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Theorem 5.2.

Given any 0<ε<10<\varepsilon<1, there exists a constant C5.1C_{5.1}, depending on ε\varepsilon, the background metric gg, the choice of Φ\Phi, and the bound ∫MeF​Φ​(F)​𝑑v​o​lg\int_{M}e^{F}\Phi(F)dvol_{g}, such that

(5.5) F+ε​ψ−2​(1+maxM⁡|R​i​c|)​φ≤C5.1.F+\varepsilon\psi-2(1+\max_{M}|Ric|)\varphi\leq C_{5.1}.

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