The asymptotically anti-de Sitter Penrose inequality for three-dimensional initial data with spherical conformal infinity

Theorem 1.1 (principal): under those hypotheses $m_{AH}\ge\frac12(r_A+r_A^3)$ with $A$ the full enclosing-area infimum, sharp; no maximality, compact topology or connectedness assumption. Equality on the stated horizon subclass identifies the original data as a spacelike hypersurface in Schwarzschild-anti-de Sitter with the same mass. Companions: the maximal case with possibly disconnected boundary, and a local inequality for small maximal vacuum conformal perturbations of Schwarzschild-anti-de Sitter using the horizon's own area. Not shown: higher dimensions, toroidal or higher-genus conformal infinity (the Lee-Neves regime), or timelikeness of the mass as a conclusion.

Theorem 1.1 (principal): under those hypotheses $m_{AH}\ge\frac12(r_A+r_A^3)$ with $A$ the full enclosing-area infimum, sharp; no maximality, compact topology or connectedness assumption. Equality on the stated horizon subclass identifies the original data as a spacelike hypersurface in Schwarzschild-anti-de Sitter with the same mass. Companions: the maximal case with possibly disconnected boundary, and a local inequality for small maximal vacuum conformal perturbations of Schwarzschild-anti-de Sitter using the horizon's own area. Not shown: higher dimensions, toroidal or higher-genus conformal infinity (the Lee-Neves regime), or timelikeness of the mass as a conclusion.