Podnoid


Podnoid


Starnoid


Starnoid


Trinoid


Trinoid

Noid Applet



This prototype applet demonstrates three classes of CMC n-noids, constant mean curvature genus-zero surfaces with asymptotically Delaunay ends:
  • Trinoids have three Delaunay ends of unduloid or nodoid type.
  • Starnoids have ends radiating from the center like a wheel.
  • Podnoids have non-coplanar end axes.

The applet sliders set the asymptotic necksizes of the ends, and the neck/bulge checkboxes toggle between a neck and bulge at the center of the surface. The necksizes range from 1/2 to -1/2. Positive necksizes are embedded unduloid ends and negative necksizes correspond to immersed nodoid ends. Press the "compute surface" button to see the surface.

The necksizes must satisfy certain inequalities in order for the surface to exist. For example, in the case of trinoids, the absolute values of the three necksizes must satisfy the spherical triangle inequalities, and in the case of nodoid ends, the weights (which depend quadratically on the necksizes) must satisfy weight balancing inequalities.