On Conformal Metrics of Constant Positive Curvature in the Plane
DOI:
https://doi.org/10.15407/mag19.01.059Анотація
Доведено три теореми про розв’язки рiвняння $\Delta u+e^{2u}=0$ в площинi. Першi двi явно описують усi увiгнутi розв’язки. Третя теорема стверджує, що дiаметр площини з метрикою з лiнiйним елементом $e^{u}|dz|$ не менше нiж $4\pi/3$, за винятком двох явно описаних сiмей розв’язкiв $u$.
Mathematical Subject Classification 2020: 35B99, 35G20, 30D15
Ключові слова:
рiвняння Лiувiлля, додатна кривина, мероморфна функцiя, сферична похiднаПосилання
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