  In this paper, we study complete minimal hypersurfaces in Riemannian
$n-$manifolds $\mathcal{M}^n$ for dimensions $4 \leq n \leq 7$, and we obtain
some results in the spirit of known work for $n=3$.
  Key contributions include extending the work of Anderson and Rodr\'{i}guez to
higher dimensions. Specifically, we show that in four-dimensional manifolds
with nonnegative sectional curvature and positive scalar curvature, two
disjoint properly embedded minimal hypersurfaces bound a slab isometric to the
product of one hypersurface with an interval.
  Our results are grounded in a maximum principle at infinity for two-sided,
parabolic, properly embedded minimal hypersurfaces in complete Riemannian
manifolds of bounded geometry, generalizing the work of Mazet in dimension
three to higher dimensions. We also leverage the recent classification of
complete two-sided stable minimal hypersurfaces by Chodosh, Li, and Stryker.
