Well-posed geometric boundary data in General Relativity, I: Conformal-mean curvature boundary data
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910940260204544 |
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| author | An, Zhongshan Anderson, Michael T. |
| author_facet | An, Zhongshan Anderson, Michael T. |
| contents | We study the local in time well-posedness of the initial boundary value problem (IBVP) for the vacuum Einstein equations in general relativity with geometric boundary conditions. For conformal-mean curvature boundary conditions, consisting of the conformal class of the boundary metric and mean curvature of the boundary, well-posedness does not hold without imposing additional angle data at the corner. When the corner angle is included as corner data, we prove well-posedness of the linearized problem in $C^{\infty}$, where the linearization is taken at any smooth vacuum Einstein metric. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posed geometric boundary data in General Relativity, I: Conformal-mean curvature boundary data An, Zhongshan Anderson, Michael T. Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry We study the local in time well-posedness of the initial boundary value problem (IBVP) for the vacuum Einstein equations in general relativity with geometric boundary conditions. For conformal-mean curvature boundary conditions, consisting of the conformal class of the boundary metric and mean curvature of the boundary, well-posedness does not hold without imposing additional angle data at the corner. When the corner angle is included as corner data, we prove well-posedness of the linearized problem in $C^{\infty}$, where the linearization is taken at any smooth vacuum Einstein metric. |
| title | Well-posed geometric boundary data in General Relativity, I: Conformal-mean curvature boundary data |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2503.12599 |