Blocki–Zwonek's convexity conjecture for Green-function sublevel sets

Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$, let $w\in\Omega$, let $G_{\Omega,w}$ denote the pluricomplex Green's function of $\Omega$ with pole at $w$, and let $\lambda$ denote Lebesgue measure. Blocki–Zwonek's conjecture. The function

$$t\longmapsto \log \lambda(\{G_{\Omega,w}<t\})$$

should be convex. The paper gives a counterexample, so the conjecture is false.