Mass-systole conjecture for generalized asymptotically flat manifolds

Let $(M,g,E)$ be a generalized asymptotically flat manifold: $(M,g)$ is a complete Riemannian $n$-manifold without boundary, with $n\geq 3$, $E$ is an asymptotically flat end, and $R(g)\in L^1(E,g)$. Define

$$\operatorname{sys}(M,g,E)=\inf\left\{\lvert\Sigma\rvert_g:\ \Sigma\text{ is a smoothly embedded hypersurface homologous to }\partial E\text{ in }M\right\}.$$

Mass-systole conjecture. If $(M,g,E)$ has nonnegative scalar curvature, then

$$m(M,g,E)\geq \frac{1}{2}\left(\frac{\operatorname{sys}(M,g,E)}{\lvert\mathbb S^{n-1}\rvert}\right)^{\frac{n-2}{n-1}}.$$

Moreover, equality holds if and only if either $(M,g)$ is isometric to Euclidean space, or there is a strictly outer-minimizing minimal $(n-1)$-sphere $\Sigma_h$ homologous to $\partial E$ such that the region outside $\Sigma_h$ is isometric to the half spatial Schwarzschild manifold with mass $m>0$.

This conjecture seeks a mass-capacity-type inequality for generalized asymptotically flat manifolds and is motivated by applications to spatial slices of the extreme Reissner–Nordström spacetime. The supplied source does not state whether the conjecture has been resolved.