Corollary 20.3.36C5512844A274

Corollary 20.3.36.C5512844A274 Let $\Omega $ and $T$ be as in theorem 20.3.35, let $\mathrm{d}V$ be a smooth positive volume form on $Y$, and let $0\leq f\in L^ p(\mathrm{d}V)$, $p>1$, with $\int _ Y f\, \mathrm{d}V>0$. For every $\lambda >0$ there is a unique $a\in \mathrm{PSH}(Y,\Omega )$ with $a\sim T$ and

There are also a constant $c>0$ and $a\in \mathrm{PSH}(Y,\Omega )$ with $a\sim T$ and $\mathrm{MA}^{\mathrm{ext}}_\Omega (a)=cf\, \mathrm{d}V$, and the constant $c$ is unique.