A positive mass theorem for low-regularity metrics

Abstract

We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W_{\mathrm{loc}}^{2,n/2}(M)$. We argue that this is the largest class of metrics with scalar curvature a positive a.c. measure for which the positive mass theorem may be proved by our methods.

arXiv commentAnnouncement, 4 pages, comments welcome

References in corpus (2)

• On the positive mass theorem for manifolds with corners
• A positive mass theorem for Lipschitz metrics with small singular sets

Cited by in corpus (2)

• A positive mass theorem for low-regularity Riemannian metrics
• The positive mass theorem for manifolds with distributional curvature