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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Liouville equation and spherical convex polytopes


Authors: Feng Luo and Gang Tian
Journal: Proc. Amer. Math. Soc. 116 (1992), 1119-1129
MSC: Primary 53C21; Secondary 52A55
DOI: https://doi.org/10.1090/S0002-9939-1992-1137227-5
MathSciNet review: 1137227
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Abstract: We study the Liouville equation $ \Delta u = - {e^{2u}}$ in the complex plane with prescribed singularities and obtain a necessary and sufficient condition for the existence of the solution. The proof is based on the continuity method and a uniqueness theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1137227-5
Article copyright: © Copyright 1992 American Mathematical Society

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