ScalingStacks

Theorem 2.4. On a fixed $(X,\omega)$, there are positive constants $\alpha$, $C$ depending only on $X,\omega$, such that

$$\int_{X}e^{-\alpha\phi}\omega_{X}^{n}\leq C,\quad\forall\phi\in PSH(X,\omega)\text{ with }\sup\phi=0.$$