Marginally outer trap surface with capillary boundary and rigidity of initial data sets
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916857159614464 |
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| author | Lee, Sanghun |
| author_facet | Lee, Sanghun |
| contents | In this paper, we present the several rigidity results of initial data sets with boundary when a marginally outer trap surface (MOTS) with capillary boundary is embedded. First, we establish estimates for the area of a MOTS with capillary boundary. Next, we prove a rigidity for 3-dimensional initial data sets with boundary. Furthermore, we extend our results from the 3-dimensional case to the high dimensional initial data sets using the Yamabe constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marginally outer trap surface with capillary boundary and rigidity of initial data sets Lee, Sanghun Differential Geometry 53C24, 53A10, 53C21 In this paper, we present the several rigidity results of initial data sets with boundary when a marginally outer trap surface (MOTS) with capillary boundary is embedded. First, we establish estimates for the area of a MOTS with capillary boundary. Next, we prove a rigidity for 3-dimensional initial data sets with boundary. Furthermore, we extend our results from the 3-dimensional case to the high dimensional initial data sets using the Yamabe constant. |
| title | Marginally outer trap surface with capillary boundary and rigidity of initial data sets |
| topic | Differential Geometry 53C24, 53A10, 53C21 |
| url | https://arxiv.org/abs/2507.16617 |