Positive mass conjecture for asymptotically hyperbolic initial data

Prove that the mass of an asymptotically hyperbolic vacuum initial data set is nonnegative, with equality only when the data arise as a Cauchy hypersurface of Minkowski space, under general assumptions beyond currently known decay conditions.

Background

The paper defines the mass functional for asymptotically hyperbolic (AH) manifolds and recalls a long-standing conjecture asserting positivity of this mass, with rigidity for Minkowski space.

The authors note that, despite supporting evidence, the conjecture has only been proven under specific decay conditions in three-dimensional vacuum settings, and they study sharpness of decay hypotheses by exhibiting negative mass at critical decay, indicating the importance of decay rates in the conjecture.