Elliptic functions and nonexistence of complete minimal surfaces of certain type

Chen, Chi Cheng

doi:10.1090/S0002-9939-1980-0565356-5

Elliptic functions and nonexistence of complete minimal surfaces of certain type
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Proc. Amer. Math. Soc. 79 (1980), 289-293 Request permission

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

Quelques applications l’analyse complexe aux surface d’aire minima

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