Complete minimal surfaces in 𝑅³ of genus one and four planar embedded ends

Costa, Celso J.

doi:10.1090/S0002-9939-1993-1160295-2

Complete minimal surfaces in $\textbf {R}^ 3$ of genus one and four planar embedded ends
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Proc. Amer. Math. Soc. 119 (1993), 1279-1287 Request permission

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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Éléments de la théorie des fonctions elliptiques