A CR structure with blowing up solutions to the CR Yamabe problem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917892963958784 |
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| author | Afeltra, Claudio Pinamonti, Andrea |
| author_facet | Afeltra, Claudio Pinamonti, Andrea |
| contents | We prove the existence of a CR structure on $S^3$ such that the set of solutions to the CR Yamabe problem is not compact and admits a blowing-up sequence. Such CR structure is built deforming the standard CR structure of $S^3$ in the direction of the Rossi sphere CR structure on small balls, and the existence of the blowing-up sequence of solutions is proved through the Lyapunov-Schmidt method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08782 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A CR structure with blowing up solutions to the CR Yamabe problem Afeltra, Claudio Pinamonti, Andrea Analysis of PDEs Differential Geometry We prove the existence of a CR structure on $S^3$ such that the set of solutions to the CR Yamabe problem is not compact and admits a blowing-up sequence. Such CR structure is built deforming the standard CR structure of $S^3$ in the direction of the Rossi sphere CR structure on small balls, and the existence of the blowing-up sequence of solutions is proved through the Lyapunov-Schmidt method. |
| title | A CR structure with blowing up solutions to the CR Yamabe problem |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2501.08782 |