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Chen-Gackstatter Surfaces

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The Chen–Gackstatter surfaces, constructed in 1982, are a family of complete orientable minimal surfaces of that generalize Enneper's minimal surface by adding handles that increase its topological genus or by adding -fold dihedral symmetry. In cases with genus values greater than one, the formulas for the surfaces involve generalized hypergeometric functions.

Contributed by: Enrique Zeleny (June 2014)
Open content licensed under CC BY-NC-SA

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References

[1] M. Weber. "Chen–Gackstatter Surface." Minimal Surface Archive. (Jun 12, 2014) www.indiana.edu/~minimal/archive/Tori/Tori/Chen-Gackstatter/web/index.html.

[2] E. C. Thayer, "Higher-Genus Chen–Gackstatter Surfaces and the Weierstrass Representation for Surfaces of Infinite Genus," Experimental Mathematics, 4(1), 1995 pp. 19–39. doi:10.1080/10586458.1995.10504305.

[3] F. J. López and F. Martín, "Complete Minimal Surfaces in ," Publicacions Matematiques, 43(2), 1999 pp. 341–449. www.ugr.es/~fmartin/dvi/survey.pdf.

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