The Penrose conjecture for initial data sets satisfying a 2-convexity condition

2026/07/22 by Conghan Dong · 1 citation
Mathematics · Physics and Astronomy · #gr-qc #math.DG

paper · pdf

v2: connected horizon assumption added; references added;

arxiv created 2026/07/30 · arxiv updated 2026/08/03

Abstract

Let (M³, g, k) be a smooth, connected, asymptotically flat initial data set with connected outermost past apparent horizon Σ. We prove the Penrose conjecture, namely that m_ADM(g) ≥ √((|Σ|)/(16 π)) , under the assumptions of the dominant energy condition and the 2-convexity condition that the sum of the two smallest eigenvalues of k is nonnegative. The main tool is the σ-inverse mean curvature flow, together with a monotonicity formula developed in \citeDong26SigmaIMCF.

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• The Penrose inequality with charge for 2-convex initial data sets

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