Prescribed Ricci curvature near an Einstein manifold with boundary
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910890200137728 |
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| author | Delay, Erwann |
| author_facet | Delay, Erwann |
| contents | Let (M, g) be a compact Einstein Riemannian manifold with boundary. We show that under certain conditions, the map that associates to a metric on M its Ricci curvature, its induced conformal class on the boundary, and its mean curvature on the boundary is locally invertible near g. The contravariant Ricci operator, as well as other operators such as the Einstein operator, are also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prescribed Ricci curvature near an Einstein manifold with boundary Delay, Erwann Differential Geometry Let (M, g) be a compact Einstein Riemannian manifold with boundary. We show that under certain conditions, the map that associates to a metric on M its Ricci curvature, its induced conformal class on the boundary, and its mean curvature on the boundary is locally invertible near g. The contravariant Ricci operator, as well as other operators such as the Einstein operator, are also studied. |
| title | Prescribed Ricci curvature near an Einstein manifold with boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.18452 |