## Minimal Surfaces: Catenoid

### Example of a Convex Optimization Problem

Drag mouse to rotate model. Hold *shift* key or use mouse wheel
to zoom it.
Given a domain in *R*^{2} and an embedding of its boundary in
*R*^{3}, the minimal surface problem is to
find an embedding of the entire surface into *R*^{3}
that is consistent with the boundary embedding and has minimual surface area.
This problem is a
convex optimization problem. To see the AMPL file that was used to generate
the surface shown at right, click here.

LOQO was used to compute the minimal surface shown at right.
To get a better feel
for the surface, set it in motion by dragging and releasing the object.

Here are some other interesting minimal surfaces:

*Updated* 2012 Dec 2