Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 260-06. The nonmaximal anti-de Sitter Penrose Inequality and original-data rigidity
Manuscript map · lines 7555–7564
OpenAI@2026-10-07#rem:oai-p-260-06
Authors: OpenAI. Family 260.
Title: The nonmaximal anti-de Sitter Penrose Inequality and original-data rigidity.
Abstract: We prove the spacetime Penrose Inequality for smooth three-dimensional initial-data exteriors with one spherical asymptotically anti-de Sitter end, satisfying the stated decay and integrability assumptions, the dominant energy condition, and a compact weakly future outer trapped boundary. We assume that the hyperbolic metric four-flux is future timelike; its Lorentz norm is the mass, and the area is the infimum over full enclosing cuts. On the connected outermost, outer area-minimizing horizon subclass, equality characterizes the original data as a spacelike hypersurface in Schwarzschild–anti-de Sitter spacetime with matching metric mass. No maximality, evolution, or auxiliary solvability assumption is used.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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