The positive mass theorem for non-spin manifolds with distributional curvature

Abstract

We prove the positive mass theorem for manifolds with distributional curvature which have been studied in \cite{Lee2015} without spin condition. In our case, the manifold $M$ has asymptotically flat metric $g\in C^0\bigcap W_{-q}^{1,p}$, $p>n$, $q>\frac{n-2}{2}$. We show that the generalized ADM mass $m_{ADM}(M,g)$ is non-negative as long as $q=n-2$, and $g$ has non-negative distributional scalar curvature, bounded curvature in the Alexandrov sense with its distributional Ricci curvature belonging to certain weighted Lebesgue space and some extra conditions.

arXiv comment18 pages

References in corpus (2)

• On the positive mass theorem for manifolds with corners
• Ricci flow on asymptotically Euclidean manifolds