On Conformal Metrics of Constant Positive Curvature in the Plane
We prove three theorems about solutions of $\Delta u+e^{2u}=0$ in the plane. The first two describe explicitly all concave and quasiconcave solutions. The third theorem says that the diameter of the plane with respect to the metric with line element $e^{u}|dz|$ is at least $4\pi/3$, except for two e...
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| Datum: | 2023 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/996 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | We prove three theorems about solutions of $\Delta u+e^{2u}=0$ in the plane. The first two describe explicitly all concave and quasiconcave solutions. The third theorem says that the diameter of the plane with respect to the metric with line element $e^{u}|dz|$ is at least $4\pi/3$, except for two explicitly described families of solutions $u$.
Mathematical Subject Classification 2020: 35B99, 35G20, 30D15
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