The Schwarz symmetrization conjecture for residue Monge–Ampère mass

Let $u$ be an $S^1$-invariant plurisubharmonic function with a single pole at the origin on a balanced domain $\Omega$, and let $\hat u$ be its symmetrization. The residue Monge–Ampère mass is denoted by $\tau_u(0)$.

Schwarz symmetrization conjecture. One has

$$\tau_{\hat u}(0) \leq \tau_u(0).$$

For $S^1$-invariant plurisubharmonic functions with a single pole at the origin, the residue mass is well defined, so this asks whether Schwarz symmetrization always decreases it. The supplied text does not state whether the inequality is known or remains open.