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 β-weak (β∈(0, 1/2)) sense of {MR4685089} on an asymptotically flat $n-$manifold with a W1,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 β-weak sense and the time. Then we prove that the lower bound of the distributional scalar curvature of a W1, p metric coincides with the lower bound of the scalar curvature in the β-weak sense at infinity.