Our work investigates varifolds $\Sigma \subset M$ in a Riemannian manifold, with arbitrary codimension and bounded mean curvature, contained an open domain $\Omega$. Under mild assumptions on the curvatures of $M$ $\partial \Omega$, also allowing for certain singularities we prove barrier principle at infinity, namely show that distance $\Sigma$ to \Omega$ is attained \Sigma$. theorem conseque...