Symmetric Fournoids

Constant mean curvature surfaces in euclidean 3-space

Fournoids are four-punctured spheres with asymptotically Delaunay ends. These fournoids are constructed by lifting a trinoid-like surface on a three-punctured sphere to a multiply-punctured sphere [2].

Coplanar “airplane” fournoid with three different end weights
Coplanar “cross” fournoid with two different end weights
Coplanar “wheel” fournoid with equal end weights
Noncoplanar “tripod” fournoid with two different end weights
Tetranoid with tetrahedral symmetry

References

  1. N. Schmitt, M. Kilian, S.-P. Kobayashi and W. Rossman, Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms, J. Lond. Math. Soc. (2) 75 (2007), no. 3, 563–581.
  2. N. Schmitt, Constant mean curvature n-noids with platonic symmetries, arxiv:math/0702469, 2007.