Abstract
In this paper, we consider conformal flat metrics on R4 with an asymptotically hyperbolic (AH) end and possible isolated conic singularities. We define a mass term of the AH end. If the σ2 curvature has lower bound σ2≥32, we prove an inequality relating the mass and contributions from singularities. We also classify sharp cases, which is the standard hyperbolic 4-space H4 when no singularity occurs. It is worth noting that our curvature condition implies non-positive energy density.
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