Helicoid with a Hole

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Obtained in terms of elliptic functions [2], this minimal surface has two helicoidal ends consisting of a helicoid with a hole and handle; it has genus one and it is invariant under a one-dimensional group of translations.

Contributed by: Enrique Zeleny (June 2014)
Based on a program by: Paul Nylander
Open content licensed under CC BY-NC-SA




[1] D. Hoffman, H. Karcher, and F. Wei. "The Genus One Helicoid and the Minimal Surfaces that Led to Its Discovery in Global Analysis and Modern Mathematics." (1993) www.gang.umass.edu/preprint/documents/gang3-16.pdf.gz.

[2] M. Weber. "The genus One Helicoid as a Limit of Screw-Motion Invariant Helicoids with Handles." (Jan 6, 2003) www.indiana.edu/~minimal/research/heliclay.pdf.

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