ScalingStacks

Theorem 2.9 . [0085]

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Theorem 2.9.

(Uniform Skoda estimate) Suppose the measures d​μtd\mu_{t} on XtX_{t} satisfy a uniform upper bound of class (ai)(a_{i}). Then there are uniform positive constants α\alpha and AA, such that

∫Xte−α​u​d​μt≤A,∀u∈P​S​H​(Xt,ωt)​ with ​supXtu=0.\int_{X_{t}}e^{-\alpha u}d\mu_{t}\leq A,\quad\forall u\in PSH(X_{t},\omega_{t})\text{ with }\sup_{X_{t}}u=0.

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