Static asymptotically hyperbolic vacuum spacetimes with negative Lambda are stable attractors of the Ricci-harmonic flow precisely when a positive mass theorem holds nearby.
Sobolev-Class Asymptotically Hyperbolic Manifolds and the Yamabe Problem
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Static Vacuum Spacetimes with $\Lambda<0$ as Attractors of the Ricci-Harmonic Flow
Static asymptotically hyperbolic vacuum spacetimes with negative Lambda are stable attractors of the Ricci-harmonic flow precisely when a positive mass theorem holds nearby.