A positive mass theorem for low-regularity metrics

James D. E. Grant, Nathalie Tassotti

Published 2012-05-07Version 1

We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W^{2, n/2}_{\mathrm{loc}}(M)$. 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.