2024/05/16 by Yuqiao Li, Li, Yuqiao
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2405.09750
openalex publication_date 2024/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the scalar curvature in the distributional sense of \citeMR3366052 and the scalar curvature lower bound in the β-weak (β∈(0, (1)/(2))) sense of \citeMR4685089 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.