On Conformal Metrics of Constant Positive Curvature in the Plane

Автор(и)

  • Walter Bergweiler Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Heinrich-Hecht-Platz 6, 24118 Kiel, Germany
  • Alexandre Eremenko Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
  • James Langley School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

DOI:

https://doi.org/10.15407/mag19.01.059

Ключові слова:

рiвняння Лiувiлля, додатна кривина, мероморфна функцiя, сферична похiдна

Анотація

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

Посилання

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Bergweiler, W.; Eremenko, A.; Langley, J. On Conformal Metrics of Constant Positive Curvature in the Plane. Журн. мат. фіз. анал. геом. 2023, 19, 59-73.

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