Existence of complete conformal metrics on $\mathbb{R}^n$ with prescribed Q-curvature
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916667728068608 |
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| author | Li, Mingxiang Ma, Biao |
| author_facet | Li, Mingxiang Ma, Biao |
| contents | Given a smooth function $f(x)$ on $\mathbb{R}^n$ which is positive somewhere and satisfies $f(x)=O(|x|^{-l})$ for any $l>\frac{n}{2}$, we show that there exists a complete and conformal metric $g=e^{2u}|dx|^2$ with finite total Q-curvature such that its Q-curvature equals to $f(x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of complete conformal metrics on $\mathbb{R}^n$ with prescribed Q-curvature Li, Mingxiang Ma, Biao Differential Geometry Analysis of PDEs Given a smooth function $f(x)$ on $\mathbb{R}^n$ which is positive somewhere and satisfies $f(x)=O(|x|^{-l})$ for any $l>\frac{n}{2}$, we show that there exists a complete and conformal metric $g=e^{2u}|dx|^2$ with finite total Q-curvature such that its Q-curvature equals to $f(x)$. |
| title | Existence of complete conformal metrics on $\mathbb{R}^n$ with prescribed Q-curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2503.23689 |