Monotonicity conjecture for sublevel volumes of the pluricomplex Green function

Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$, let $w otinOmega$, and let $G_{Omega,w}$ denote its pluricomplex Green function. Consider the sublevel-volume function

$$tlongmapsto e^{-2nt}\lambda({G_{\Omega,w}<t})$$

Monotonicity conjecture. If $\Omega$ is pseudoconvex in $\mathbb C^n$ then this function is non-decreasing on $(-\infty,0]$. The conjecture is proved in dimension one; in arbitrary dimension it is equivalent to a pluricomplex isoperimetric inequality for bounded strongly pseudoconvex domains with smooth boundary.