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1997 Compact constant mean curvature surfaces with low genus
Karsten Große-Brauckmann, Konrad Polthier
Experiment. Math. 6(1): 13-32 (1997).

Abstract

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.

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Karsten Große-Brauckmann. Konrad Polthier. "Compact constant mean curvature surfaces with low genus." Experiment. Math. 6 (1) 13 - 32, 1997.

Information

Published: 1997
First available in Project Euclid: 13 March 2003

zbMATH: 0898.53009
MathSciNet: MR1464579

Subjects:
Primary: 53A10
Secondary: 49Q05

Rights: Copyright © 1997 A K Peters, Ltd.

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Vol.6 • No. 1 • 1997
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