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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24828 |
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| _version_ | 1866917178187448320 |
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| author | Ghosh, Mrityunjoy Hyder, Ali |
| author_facet | Ghosh, Mrityunjoy Hyder, Ali |
| contents | In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness arguments, we derive necessary and sufficient conditions for the existence of radial normal solutions to a singular $Q$-curvature problem. Moreover, under suitable assumptions on the $Q$-curvature, we obtain uniform bounds on the total $Q$-curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bol's type inequality for singular metrics and its application to prescribing $Q$-curvature problems Ghosh, Mrityunjoy Hyder, Ali Analysis of PDEs In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness arguments, we derive necessary and sufficient conditions for the existence of radial normal solutions to a singular $Q$-curvature problem. Moreover, under suitable assumptions on the $Q$-curvature, we obtain uniform bounds on the total $Q$-curvature. |
| title | Bol's type inequality for singular metrics and its application to prescribing $Q$-curvature problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.24828 |