The full-mass characterization of the Monge–Ampère mass for the associated plurisubharmonic singularity

Assume $u\text{?}$ is an $\operatorname{PSH}({\mathbb{P}}^{n-1},\omega_0)$ function, and let $\varphi$ be defined as in the source's equation. Let $e_n(\varphi)$ denote its Monge–Ampère mass, and let $\mathcal{E}(\omega_0)$ be the set of $\omega_0$-plurisubharmonic functions of full mass.

Full-mass conjecture. $e_n(\varphi)=1$ if and only if $u\in\mathcal{E}(\omega_0)$.

This is proposed as a local analogue of a result of Darvas. The cited reference of Guedj and Zeriahi introduces the full-mass class $\mathcal{E}(\omega_0)$; the conjecture concerns when the associated local singularity has normalized Monge–Ampère mass one.