Foliation of area minimizing hypersurfaces in asymptotically flat
manifolds and Schoen's conjecture
Foliation of area minimizing hypersurfaces in asymptotically flat
manifolds and Schoen's conjecture
In this paper, we demonstrate that any asymptotically flat manifold $(M^n, g)$ with $4\leq n\leq 7$ can be foliated by a family of area-minimizing hypersurfaces, each of which is asymptotic to Cartesian coordinate hyperplanes defined at an end of $(M^n, g)$. As an application of this foliation, we show that …