ScalingStacks

Theorem 2.1. (cf. [40, Thm 3.1]) If $\phi$ is psh on $B_{2}\subset\mathbb{C}^{n}$, with $\int_{B_{2}}|\phi|\omega_{E}^{n}\leq 1$ with respect to the standard Euclidean metric $\omega_{E}$, then there are dimensional constants $\alpha$, $C$, such that

$$\log\int_{B_{1}}e^{-\alpha\phi}\omega_{E}^{n}\leq C.$$