Finite Riemann

This surface was first discussed by Hoffman and Karcher. It shows the attempt to make an embedded minimal sphere with three ends. The two catenoidal ends are parallel catenoid ends, but the planar end must necessarily intersect the two other ends, because, by the theorem of López and Ros, such a surface cannot be embedded.

The surface comes in a 1-parameter family which illustrates nicely the López-Ros deformation utilized in the proof of the theorem mentioned above.

• Riemann's Minimal Surface
• Mathematica Notebook