Scalar curvature lower bounds on asymptotically flat manifolds

In this paper, we take into account the scalar curvature in the distributional sense ofIn this paper, we take into account the scalar curvature in the distributional sense of [14] and the scalar curvature lower bound in the [Formula: see text]weak [Formula: see text] sense of [6] on an asymptotically flat [Formula: see text]-manifold with a [Formula: see text] metric. Firstly, we demonstrate that the scalar curvature lower bound under the Ricci-DeTurck flow depends on the scalar curvature lower bound in the [Formula: see text]weak sense and the time. Then we prove that the lower bound of the distributional scalar curvature of a [Formula: see text] metric coincides with the lower bound of the scalar curvature in the [Formula: see text]weak sense.