An area growth estimate of the Liouville equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866909342021713920 |
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| author | Cai, Xiaohan Lai, Mijia Zhang, Chilin |
| author_facet | Cai, Xiaohan Lai, Mijia Zhang, Chilin |
| contents | We establish an area growth estimate for solutions that are bounded from above of the Liouville equation $Δu+K e^{2u}=0$ with a positive pinched curvature $0<λ\leq K\leqΛ$. As an application, we provide a new proof of Eremenko-Gui-Li-Xu's result in [EGLX]. We also classify solutions with an upper bound in the half plane with the boundary having constant geodesic curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An area growth estimate of the Liouville equation Cai, Xiaohan Lai, Mijia Zhang, Chilin Analysis of PDEs We establish an area growth estimate for solutions that are bounded from above of the Liouville equation $Δu+K e^{2u}=0$ with a positive pinched curvature $0<λ\leq K\leqΛ$. As an application, we provide a new proof of Eremenko-Gui-Li-Xu's result in [EGLX]. We also classify solutions with an upper bound in the half plane with the boundary having constant geodesic curvature. |
| title | An area growth estimate of the Liouville equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.19327 |