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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2306.15322 |
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| _version_ | 1866913896784199680 |
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| author | Kumar, Sameer |
| author_facet | Kumar, Sameer |
| contents | Given any asymptotically flat 3-manifold $(M,g)$ with smooth, non-empty, compact boundary $Σ$, the conformal conjecture states that for every $δ>0$, there exists a metric $g' = u^4 g$, with $u$ a harmonic function, such that the area of outermost minimal area enclosure $\tildeΣ_{g'}$ of $Σ$ with respect to $g'$ is less than $δ$. Recently, the conjecture was used to prove the Riemannian Penrose inequality for black holes with zero horizon area, and was proven to be true under the assumption of existence of only a finite number of minimal area enclosures of boundary $Σ$, and boundedness of harmonic function $u$. We prove the conjecture assuming only the boundedness of $u$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15322 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proof of the bounded conformal conjecture Kumar, Sameer Differential Geometry Given any asymptotically flat 3-manifold $(M,g)$ with smooth, non-empty, compact boundary $Σ$, the conformal conjecture states that for every $δ>0$, there exists a metric $g' = u^4 g$, with $u$ a harmonic function, such that the area of outermost minimal area enclosure $\tildeΣ_{g'}$ of $Σ$ with respect to $g'$ is less than $δ$. Recently, the conjecture was used to prove the Riemannian Penrose inequality for black holes with zero horizon area, and was proven to be true under the assumption of existence of only a finite number of minimal area enclosures of boundary $Σ$, and boundedness of harmonic function $u$. We prove the conjecture assuming only the boundedness of $u$. |
| title | Proof of the bounded conformal conjecture |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2306.15322 |