Compact Constant Mean Curvature Surfaces with Low Genus
- 1 January 1997
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 6 (1) , 13-32
- https://doi.org/10.1080/10586458.1997.10504348
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.Keywords
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