## Experimental Mathematics

### Computing discrete minimal surfaces and their conjugates

#### Abstract

We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations.

Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.

#### Article information

Source
Experiment. Math., Volume 2, Issue 1 (1993), 15-36.

Dates
First available in Project Euclid: 3 September 2003