Horgan Surface

The Horgan surface would be an embedded minimal surface of genus 2 with three ends, contradicting the Hoffman-Meeks conjecture. This surface comes in a 1-parameter family, but for none of it the period problem can be completely solved. For some values, the gaps are as apparent as in the picture on the right, for others, the surface looks perfectly fine, because the gap is smaller than the resolution of the image.

• Costa surface
• Mathematica Notebook