Higher order Bol's inequality and its applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917642974003200 |
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| author | Li, Mingxiang Wei, Juncheng |
| author_facet | Li, Mingxiang Wei, Juncheng |
| contents | In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with respect to Q-curvature. Finally, we make use of these results to give some sufficient and necessary conditions for the existence of solutions to some conformally invariant equations which answers an open problem raised by Hyder-Martinazzi (2021, JDE). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher order Bol's inequality and its applications Li, Mingxiang Wei, Juncheng Differential Geometry Analysis of PDEs 53C18, 35A23 In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with respect to Q-curvature. Finally, we make use of these results to give some sufficient and necessary conditions for the existence of solutions to some conformally invariant equations which answers an open problem raised by Hyder-Martinazzi (2021, JDE). |
| title | Higher order Bol's inequality and its applications |
| topic | Differential Geometry Analysis of PDEs 53C18, 35A23 |
| url | https://arxiv.org/abs/2308.11388 |