Scalar curvature lower bounds on asymptotically flat manifolds

In this paper, we consider the scalar curvature in the distributional sense of MR3366052 and the scalar curvature lower bound in the -weak ( (0, 12) ) sense of MR4685089 on an asymptotically flat n-manifold with a W^1, p (p>n) metric. We first show that the scalar curvature lower bound under the Ricci-DeTurck flow depends on the scalar curvature lower bound in the -weak sense and the time. Then we prove that the lower bound of the distributional scalar curvature of a W^1, p metric coincides with the lower bound of the scalar curvature in the -weak sense at infinity.