1205.1302 (James D. E. Grant et al.)

A positive mass theorem for low-regularity metrics    [PDF]

James D. E. Grant, Nathalie Tassotti

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.

View original: http://arxiv.org/abs/1205.1302