The σ-inverse mean curvature flow and the generalized Penrose conjecture

2026/05/26 by Conghan Dong · 1 citation
Mathematics · #math.DG #gr-qc

paper · pdf

Abstract

Let (M³, g, k) be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let m denote its ADM mass. The generalized Penrose conjecture asserts that the area of an outermost generalized apparent horizon N⊂ M satisfies |N| ≤ 16 πm². In this paper, we establish this inequality for each connected component of N in the case where k is proportional to the metric g. Our approach is based on a new geometric evolution, which we call the σ-inverse mean curvature flow, together with a novel monotonicity formula that may be of independent interest.

Cited by

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

Related

• The Penrose conjecture for initial data sets satisfying a 2-convexity condition
• On the Penrose Inequality
• On the Isoperimetric Riemannian Penrose Inequality
• The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary
• Monotone Quantities for p-Harmonic functions and the Sharp p-Penrose inequality