Obstructions to prescribed Q-curvature of complete conformal metrics on $\mathbb{R}^n$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915607586275328 |
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| author | Li, Mingxiang |
| author_facet | Li, Mingxiang |
| contents | We provide some obstructions to the prescribed Q-curvature problem for the complete conformal metrics on $\mathbb{R}^n$ with finite total Q-curvature. One of them is a Bonnet-Mayer type theorem with respect to Q-curvature. Others are related to the decay rate of the prescribed functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Obstructions to prescribed Q-curvature of complete conformal metrics on $\mathbb{R}^n$ Li, Mingxiang Differential Geometry Analysis of PDEs 53C18, 58J90 We provide some obstructions to the prescribed Q-curvature problem for the complete conformal metrics on $\mathbb{R}^n$ with finite total Q-curvature. One of them is a Bonnet-Mayer type theorem with respect to Q-curvature. Others are related to the decay rate of the prescribed functions. |
| title | Obstructions to prescribed Q-curvature of complete conformal metrics on $\mathbb{R}^n$ |
| topic | Differential Geometry Analysis of PDEs 53C18, 58J90 |
| url | https://arxiv.org/abs/2401.03457 |