The LCF Liouville conjecture for nonnegative scalar curvature

Let $(M^n,g)$, $n\geq 3$, be a complete, locally conformally flat manifold with scalar curvature $R\geq 0$, and let $\Phi:M^n\to S^n$ be a conformal map. LCF Liouville conjecture. The map $\Phi$ is injective and $\partial\Phi(M)$ has zero Newtonian capacity. This conjecture concerns the rigidity of conformal maps from complete locally conformally flat manifolds with nonnegative scalar curvature. It is known for $n\geq 7$, and the paper states that its remaining cases follow from the positive mass conjecture with arbitrary ends and related results.