The $σ$-inverse mean curvature flow and the generalized Penrose conjecture
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911718120095744 |
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| author | Dong, Conghan |
| author_facet | Dong, Conghan |
| contents | Let $(M^3, g, \mathbf{k})$ 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 $N\subset M$ satisfies $|N| \leq 16 πm^2$. In this paper, we establish this inequality for each connected component of $N$ in the special case where $\mathbf{k}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26504 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $σ$-inverse mean curvature flow and the generalized Penrose conjecture Dong, Conghan Differential Geometry General Relativity and Quantum Cosmology Let $(M^3, g, \mathbf{k})$ 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 $N\subset M$ satisfies $|N| \leq 16 πm^2$. In this paper, we establish this inequality for each connected component of $N$ in the special case where $\mathbf{k}$ 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. |
| title | The $σ$-inverse mean curvature flow and the generalized Penrose conjecture |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.26504 |