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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.07824 |
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| _version_ | 1866913686423076864 |
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| author | Almaraz, Sergio Wang, Shaodong |
| author_facet | Almaraz, Sergio Wang, Shaodong |
| contents | On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe conformal invariant, we prove that this set is a priori bounded in the three-dimensional case and in the locally conformally flat with umbilical boundary case in any dimension not less than three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature Almaraz, Sergio Wang, Shaodong Differential Geometry Analysis of PDEs 53C21, 35J66, 35R01 On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe conformal invariant, we prove that this set is a priori bounded in the three-dimensional case and in the locally conformally flat with umbilical boundary case in any dimension not less than three. |
| title | A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature |
| topic | Differential Geometry Analysis of PDEs 53C21, 35J66, 35R01 |
| url | https://arxiv.org/abs/2502.07824 |