Chen-Gackstatter Surfaces

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.


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[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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