Chen-Gackstatter Surfaces

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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




[1] M. Weber. "Chen–Gackstatter Surface." Minimal Surface Archive. (Jun 12, 2014)

[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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.