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Proceedings of the American Mathematical Society

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

 

 

Complete minimal surfaces in $ {\bf R}\sp 3$ of genus one and four planar embedded ends


Author: Celso J. Costa
Journal: Proc. Amer. Math. Soc. 119 (1993), 1279-1287
MSC: Primary 53A10; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1993-1160295-2
MathSciNet review: 1160295
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Abstract: By using elliptic functions and Weierstrass representation we construct a one-parameter family of complete minimal surfaces in $ {{\mathbf{R}}^3}$ with genus one and four planar embedded ends. These surfaces are critical points of the Willmore functional.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1160295-2
Article copyright: © Copyright 1993 American Mathematical Society