The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915333083758592 |
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| author | Kishida, Riku |
| author_facet | Kishida, Riku |
| contents | In this paper, we focus on a marginally trapped submanifold $f:Σ^n\to M^{n+2}_1$ in a Lorentzian manifold $M^{n+2}_1$. We show that $f$ lies in a certain null hypersurface $\mathcal{N}_f^{n+1}$ in $M^{n+2}_1$ and $f$ has a locally volume-maximizing property in $\mathcal{N}^{n+1}_f$ if $M^{n+2}_1$ satisfies the null energy condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07093 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition Kishida, Riku Differential Geometry Primary 53C42, Secondly 53B30, 53C50 In this paper, we focus on a marginally trapped submanifold $f:Σ^n\to M^{n+2}_1$ in a Lorentzian manifold $M^{n+2}_1$. We show that $f$ lies in a certain null hypersurface $\mathcal{N}_f^{n+1}$ in $M^{n+2}_1$ and $f$ has a locally volume-maximizing property in $\mathcal{N}^{n+1}_f$ if $M^{n+2}_1$ satisfies the null energy condition. |
| title | The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition |
| topic | Differential Geometry Primary 53C42, Secondly 53B30, 53C50 |
| url | https://arxiv.org/abs/2506.07093 |