The higher-dimensional sharp p-Penrose inequality

Let $(M^n,g)$ be a complete, asymptotically flat manifold with non-negative scalar curvature and non-empty minimal boundary $\Sigma$, where $3\leq n\leq 7$, and assume

$$H_{n-1}(M,\Sigma)=0.$$

Here $C_p$ and $K_p$ are the quantities used in the paper's sharp $p$-Penrose inequality. Higher-dimensional sharp $p$-Penrose conjecture. Then

$$m_{\text{ADM}}\geq 2\left(\frac{C_p}{K_p}\right)^{\frac{n-2}{n-p}}.$$

Moreover, equality holds if and only if $(M,g)$ is isometric to Schwarzschild with $\Sigma$ as the horizon. This conjecture is proposed as a higher-dimensional generalization of the Riemannian Penrose inequality; the supplied text gives the dimensional range and motivation but no resolution evidence.