Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918132543651840 |
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| author | Ho, Pak Tung Shin, Jinwoo |
| author_facet | Ho, Pak Tung Shin, Jinwoo |
| contents | In this paper, the compactness of the solutions to the constant scalar curvature and constant boundary mean curvature equation is considered. Chen and Wu constructed a smooth counterexample showing that the compactness of the set of ``lower energy" solutions to the above equation fails when the dimension of the manifold is not less than 62. We prove that a smooth counterexample still exists when the dimension of the manifold is not less than 35. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_21343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu) Ho, Pak Tung Shin, Jinwoo Differential Geometry 53C21, 35J20, 35B33 In this paper, the compactness of the solutions to the constant scalar curvature and constant boundary mean curvature equation is considered. Chen and Wu constructed a smooth counterexample showing that the compactness of the set of ``lower energy" solutions to the above equation fails when the dimension of the manifold is not less than 62. We prove that a smooth counterexample still exists when the dimension of the manifold is not less than 35. |
| title | Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu) |
| topic | Differential Geometry 53C21, 35J20, 35B33 |
| url | https://arxiv.org/abs/2508.21343 |