An Algorithm for Discrete Constant Mean Curvature Surfaces

We present a new algorithm for computing discrete constant mean curvature surfaces in ℝ3. It is based on the definition of a discrete version of the conjugate surface construction for cmc surfaces. Here we solve a Plateau problem for a discrete minimal surface in S3 by computing a sequence of discrete harmonic maps F _i : S3 → S3. The definition of a discrete conjugation allows to transform this sequence to a sequence of conjugate discrete maps which converges to a discrete cmc surface in ℝ3. The algorithm is applicable to free boundary value problems for cmc surfaces and led to the recent discovery of new compact cmc surfaces.