Localized Deformation of the Scalar Curvature and the Mean Curvature
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909935186477056 |
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| author | Sheng, Hongyi |
| author_facet | Sheng, Hongyi |
| contents | On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. We prove that this result may be localized to compact subdomains in an arbitrary Riemannian manifold with boundary. This result is a generalization of Corvino's result about localized scalar curvature deformations; however, the existence part needs to be handled delicately since the linearized problem is non-variational. We also discuss generic conditions that guarantee localized deformations, and related geometric properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localized Deformation of the Scalar Curvature and the Mean Curvature Sheng, Hongyi Differential Geometry On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. We prove that this result may be localized to compact subdomains in an arbitrary Riemannian manifold with boundary. This result is a generalization of Corvino's result about localized scalar curvature deformations; however, the existence part needs to be handled delicately since the linearized problem is non-variational. We also discuss generic conditions that guarantee localized deformations, and related geometric properties. |
| title | Localized Deformation of the Scalar Curvature and the Mean Curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.08619 |