A compactification trick for the rigidity case of the positive mass theorem

Speaker: Lawrence Lo 
Affiliation: University of Münster

Abstract

Asymptotically flat manifolds with nonnegative scalar curvature are used to model galaxy systems that are contained within a compact set. The positive mass theorem asserts that the total mass for such manifolds at each end should be nonnegative, while the rigidity statement states that if any of the masses is zero, then the manifold is Euclidean space. Previous techniques for the rigidity statement appear to rely solely on the geometries at the end of the manifold with zero mass. We demonstrate that this phenomenon can be realised through a compactification trick that closes up the other ends of the manifold. Consequently, this shows that any asymptotically flat manifold with nonnegative scalar curvature and zero mass is already scalar-flat and has only one end.