Periodic k-Noids (Minimal Surfaces in the Wild II)

The k-Noids that Shireen built last winter will keep roaming the Swiss landscape, from May to August in Wülflingen. Maybe it is time to corral them. My suggestion is to build fences of catenoids. The most classical one looks like this:

Fence1

It is, technically, a translation invariant minimal surface that has two ends and genus 1 in the quotient. A simple generalization and an even simpler 90 degree rotation leeds to towers with catenoidal openings.

Fence2

If that isn’t safe enough, you can have them with double walls (i.e. with genus two in the quotient) like so

Fence3

or so:

Fence4

All these examples have many ends in the quotient. The surprise is that there also is the elusive Uninoid which only has one catenoidal end in the quotient, namely by a 180 degree screw motion:

Fence5

Here things get tricky. Michelle Hackman has found more complicated versions of this in her thesis. Here is a Uninoid that is invariant under a screw motion with quarter turn.

Fence6

Advertisements

Leave a Reply

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

WordPress.com Logo

You are commenting using your WordPress.com 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 )

Google+ photo

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

Connecting to %s