These are complete minimal surfaces of finite total curvature -8π and were completely classified by Francisco López. The most simple case occurs when both ends have parallel normals, here we have a 1-parameter family controlled by the López-Ros parameter which shrinks the catenoidal neck:

The Enneper-Weierstraß data are

G(z)=\rho\left(z-\frac1{z}\right), \qquad dh = \left(z-\frac1z\right)\, dz \ .

If one tilts the limiting normal of the catenoidal end, its flux deforms the Enneper end. Below is an example with perpendicular limiting normals of the ends:



F. López: The Classification of Complete Minimal Surfaces with Total Curvature Greater than -12π, Trans. Amer. Math. Soc. 334, 49-73, 1992

Mathematica Notebook

PoVRay Sources


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s