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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27973 |
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| _version_ | 1866918475906154496 |
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| author | Ou, Qianzhong |
| author_facet | Ou, Qianzhong |
| contents | We study the Liouville equation $\triangle u+e^{2u} =0$ in a Riemannian surface $(M, g)$ with nonnegative $Ricci$ curvature.
Under some asymptotic lower bound assumptions, we classify all the solutions to this equation, meanwhile we obtain the rigidity results for the ambient manifold.
Note that our assumptions are optimal in some sense and differ from the classical assumption of finite total curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27973 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification results of Liouville equations and rigidity of Riemannian surfaces Ou, Qianzhong Analysis of PDEs We study the Liouville equation $\triangle u+e^{2u} =0$ in a Riemannian surface $(M, g)$ with nonnegative $Ricci$ curvature. Under some asymptotic lower bound assumptions, we classify all the solutions to this equation, meanwhile we obtain the rigidity results for the ambient manifold. Note that our assumptions are optimal in some sense and differ from the classical assumption of finite total curvature. |
| title | Classification results of Liouville equations and rigidity of Riemannian surfaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.27973 |