Jorge-Meeks K-Noids

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Discovered in 1983, the Jorge and Meeks -noids are complete minimal surfaces of finite total curvature, topologically equivalent to spheres with points removed, positioned with -fold symmetry. The 2-noid is effectively a catenoid and the 3-noid is also known as the trinoid; the -noids are generalizations of the catenoid.

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


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References

[1] L. P. Jorge and W. H. Meeks III, "The Topology of Complete Minimal Surfaces of Finite Total Gaussian Curvature," Topology, 22(2), 1983 pp. 203–221.

[2] M. Weber. "Jorge-Meeks k-Noids." Minimal Surface Archive. (Sep 2013) www.indiana.edu/~minimal/archive/Spheres/Noids/Jorge-Meeks/web/index.html.

[3] H. Karcher, "Construction of Minimal Surfaces," presentation given at Surveys in Geometry (1989), University of Tokyo, 1989. www.math.uni-bonn.de/people/karcher/karcherTokyo.pdf.

[4] U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal Surfaces, 2nd ed., New York: Springer, 2010.



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