This video shows a deformation through constant mean curvature tori, starting (after a blowup) at the three-lobed Wente torus in R³, and ending at a doubly-wrapped homogeneous torus in S³. The family is shown stereographically projected to R³.

The deformation ends at a spectral genus zero torus in S³ which has two double points on the unit circle in the complex plane of the spectral parameter. At this point, the deformation jumps from spectral genus two to spectral genus zero by closing four branch points to two double points.

The flow follows the period-preserving deformation of Kilian and Schmidt [1]. This video is a remake of one of Wjatscheslaw Kewlin's [2] pioneering videos of tori deformations to Wente tori with various lobe counts.

References

1. W. Kewlin, Deformation of constant mean curvature tori in a three sphere, Universität Mannheim, 2008.
2. M. Kilian and M. U Schmidt, On the moduli of constant mean curvature cylinders of finite type in the 3-sphere, arXiv:0712:0108v2, 2008.