Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

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

Snapshots

Details

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.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
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.
Send