Experimental Mathematics

Compact constant mean curvature surfaces with low genus

Karsten Große-Brauckmann and Konrad Polthier


We describe numerical experiments that suggest the existence of certain new compact surfaces of constant mean curvature. They come in three dihedrally symmetric families, with genus ranging from 3 to 5, 7 to 10, and 3 to 9, respectively; there are further surfaces with the symmetry of the Platonic polyhedra and genera 6, 12, and 30. We use the algorithm of Oberknapp and Polthier, which defines a discrete version of Lawson's conjugate surface method.

Article information

Experiment. Math., Volume 6, Issue 1 (1997), 13-32.

First available in Project Euclid: 13 March 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12]


Große-Brauckmann, Karsten; Polthier, Konrad. Compact constant mean curvature surfaces with low genus. Experiment. Math. 6 (1997), no. 1, 13--32. https://projecteuclid.org/euclid.em/1047565281

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