Zhou's conjecture on CMC hypersurfaces in asymptotically flat manifolds

Let $M$ be an asymptotically flat manifold of low dimension, and let $c$ be a prescribed mean curvature. A closed hypersurface in $M$ has constant mean curvature $c$ when its mean curvature is everywhere equal to $c$. Zhou's conjecture. $M$ contains at least one closed hypersurface with constant mean curvature $c$ for every prescribed $c$. This conjecture extends the existence theory for closed constant-mean-curvature hypersurfaces to certain complete, non-compact asymptotically flat manifolds; the precise dimensional range and hypotheses are not specified in the supplied statement, and its resolution is therefore not established here.