Compact constant mean curvature surfaces with low genus
Große-Brauckmann, Karsten ; Polthier, Konrad
Experiment. Math., Tome 6 (1997) no. 4, p. 13-32 / Harvested from Project Euclid
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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.
Publié le : 1997-05-14
Classification:  53A10,  49Q05 
@article{1047565281,
     author = {Gro\ss e-Brauckmann, Karsten and Polthier, Konrad},
     title = {Compact constant mean curvature surfaces with low genus},
     journal = {Experiment. Math.},
     volume = {6},
     number = {4},
     year = {1997},
     pages = { 13-32},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047565281}
}

Große-Brauckmann, Karsten; Polthier, Konrad. Compact constant mean curvature surfaces with low genus. Experiment. Math., Tome 6 (1997) no. 4, pp.  13-32. http://gdmltest.u-ga.fr/item/1047565281/