{"id":"openai-math/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data","pdf":"https://github.com/openai/math/blob/main/preprints/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Penrose-inequality-for-maximal-asymptotically-hyperbolic-initial-data-October-5-2026","tags":["general-relativity","geometric-analysis","penrose-inequality"],"score":0,"title":"The Penrose inequality for maximal asymptotically hyperbolic initial data","domain":"Mathematical physics","family":"260","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove the sharp Penrose inequality for three-dimensional maximal asymptotically hyperbolic initial data with spherical conformal infinity. Under the dominant energy condition, the stated decay and integrability assumptions, and a future-timelike mass covector, the invariant mass is bounded below by the Schwarzschild–anti-de Sitter mass associated with the minimum enclosing area of a weakly future outer-trapped boundary. The boundary may be disconnected, and no restriction is imposed on the compact topology.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions"}