Ricci flow on asymptotically Euclidean manifolds

Abstract

In this paper, we prove that if an asymptotically Euclidean manifold $(M^n,g)$ under the condition that $R\ge 0$ has long time existence of Ricci flow, the mass of $(M^n,g)$ is nonnegative. In addition, we give an independent proof of positive mass theorem in dimension $3$.

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• Spinors and mass on weighted manifolds
• ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow
• Lower semicontinuity of the ADM mass in dimensions two through seven
• The positive mass theorem for non-spin manifolds with distributional curvature