Abstract
The local mass problem is solved. That is, in suitable function spaces, it is shown that for any vacuum space-time near flat space, its massm is strictly positive. The relationship to other work in the field and some discussion of the global problem is given. Our proof is, in effect, a version of critical point analysis in infinite dimensions, but detailedLpand Sobolev-type estimates are needed for the precise proof, as well as careful attention to the coordinate invariance group. For the latter, we prove a suitable slice theorem based on the use of harmonic coordinates.
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