On a Penrose-like inequality in dimensions less than eight

2017/01/17 by Stephen McCormick, Pengzi Miao, McCormick, Stephen +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1701.04805

openalex publication_date 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On an asymptotically flat manifold Mⁿ with nonnegative scalar curvature, with outer minimizing boundary Σ, we prove a Penrose-like inequality in dimensions n < 8, under suitable assumptions on the mean curvature and the scalar curvature of Σ.

Citations

• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem

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