The Riemannian isoperimetric inequality for black-hole surfaces

Let $\Sigma$ be a compact surface in an asymptotically flat manifold with nonnegative scalar curvature $R\geq0$. Let $M$ be the mass and define the Schwarzschild radius by $r_H=2M$. Riemannian isoperimetric conjecture. The surface should satisfy

$$A\geq4\pi r_H^2,$$

or equivalently

$$\sqrt{\frac{A}{16\pi}}\geq\frac{M}{2}.$$

The source describes this as weaker than the Penrose inequality and says it follows from similar techniques, but gives no definitive resolution status.