The Penrose inequality for the Gauss–Bonnet–Chern mass

Let $n$ and $q$ be integers with $n\geq 3$ and $1\leq q<n/2$. Let $(M^n,g)$ be asymptotically flat of order $\tau>(n-2q)/(q+1)$, with integrable nonnegative $q$-th Gauss–Bonnet curvature $L_{(q)}$. Let $\Gamma$ be a possibly disconnected outermost minimal hypersurface of area $A$, and let $\mathrm{m}_q$ be the $q$-th Gauss–Bonnet–Chern mass. Penrose inequality for the Gauss–Bonnet–Chern mass.

$$\mathrm{m}_q\geq\frac{1}{2^q}\left(\frac{A}{\omega_{n-1}}\right)^{\frac{n-2q}{n-1}}.$$

Moreover, equality implies that $(M,g)$ is isometric to the $q$-th Riemannian Schwarzschild manifold.

This is the Gauss–Bonnet–Chern analogue of the Riemannian Penrose inequality, with the stated Schwarzschild model attaining equality. The supplied text does not state whether the general conjecture has been resolved.