In this paper, we demonstrate that any asymptotically flat manifold \((M^{n+1}, g)\) with \(3\leqslant n\leqslant 6\) can be foliated by a family of area-minimizing hypersurfaces, each of which is asymptotic to Cartesian coordinate hyperplanes defined at an end of \((M^{n+1}, g)\) . As an application of this foliation, we show that for any asymptotically flat manifold \((M^{n+1}, g)\) with \(3\leqslant n\leqslant 6\) , nonnegative scalar curvature and positive mass, the solution of free boundary problem for area-minimizing hypersurface in coordinate cylinder \(C_{R_i}\) in \((M^{n+1}, g)\) either does not exist or drifts to infinity of \((M^{n+1}, g)\) as \(R_i\) tends to infinity. Additionally, we introduce a concept of globally minimizing hypersurface in \((M^{n+1}, g)\) , and verify a version of the Schoen’s Conjecture.
