Communications in Analysis and Geometry
Volume 24 (2016)
A positive mass theorem for asymptotically flat manifolds with a non-compact boundary
Pages: 673 – 715
We define a mass-type invariant for $n$-dimensional asymptotically flat manifolds with a non-compact boundary and prove a positive mass theorem if either $3 \leq n \leq 7$ or if $n \geq 3$ and the manifold is spin. This settles, for this class of manifolds, a question posed in a recent paper by the first author in connection with the longterm behavior of a certain Yamabe-type flow on scalar-flat compact manifolds with boundary.