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Elliptic functions and nonexistence of complete minimal surfaces of certain type


Author: Chi Cheng Chen
Journal: Proc. Amer. Math. Soc. 79 (1980), 289-293
MSC: Primary 53A10
DOI: https://doi.org/10.1090/S0002-9939-1980-0565356-5
MathSciNet review: 565356
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Abstract: It is proved that any complete minimal surfaces in $ {{\mathbf{R}}^n}(n \geqslant 3)$ with total curvature $ - 4\pi $ is conformally equivalent to the complex plane or the punctured plane, just like the case in $ {{\mathbf{R}}^3}$.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1980-0565356-5
Article copyright: © Copyright 1980 American Mathematical Society

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