On positivity of the Q-curvatures of conformal metrics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913945190662144 |
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| author | Li, Mingxiang Xu, Xingwang |
| author_facet | Li, Mingxiang Xu, Xingwang |
| contents | We mainly show that for a conformal metric $g=u^{\frac{4}{n-2m}}|dx|^2$ on $\mathbb{R}^n$ with $n\geq 2m+1$, if the higher order Q-curvature $Q^{(2m)}_g$ is positive and has slow decay barrier near infinity, the lower order Q-curvature $Q^{(2)}_g$ and $Q^{(4)}_g$ are both positive if $m$ is at least two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On positivity of the Q-curvatures of conformal metrics Li, Mingxiang Xu, Xingwang Differential Geometry Analysis of PDEs 53C18, 58J90 We mainly show that for a conformal metric $g=u^{\frac{4}{n-2m}}|dx|^2$ on $\mathbb{R}^n$ with $n\geq 2m+1$, if the higher order Q-curvature $Q^{(2m)}_g$ is positive and has slow decay barrier near infinity, the lower order Q-curvature $Q^{(2)}_g$ and $Q^{(4)}_g$ are both positive if $m$ is at least two. |
| title | On positivity of the Q-curvatures of conformal metrics |
| topic | Differential Geometry Analysis of PDEs 53C18, 58J90 |
| url | https://arxiv.org/abs/2402.16277 |