ScalingStacks

Lemma 2.5. (Concavity of $det^{1/n}$) On an open domain, suppose $u,v$ are continuous $\omega$-psh functions, with

$$\omega_{u}^{n}=f\omega^{n},\quad\omega_{v}^{n}=g\omega^{n}$$

for $f,g\in L^{\infty}$. Then for $0<s<1$, we have $\omega_{su+(1-s)v}^{n}\geq(sf^{1/n}+(1-s)g^{1/n})^{n}\omega^{n}$.