An Algorithm for Discrete Constant Mean Curvature Surfaces

. We present a new algorithm for computing discrete constant mean curvature surfaces in R 3 . 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 S 3 by computing a sequence of discrete harmonic maps F i : S 3 ! S 3 . 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 R 3 . The algorithm is applicable to free boundary value problems for cmc surfaces and led to the recent discovery of new compact cmc surfaces. 1. Introduction Surfaces with constant mean curvature (cmc surfaces) are the mathematical abstraction of physical soap films and soap bubbles. Such surfaces behave like rubber bands which try to contract under their surface tension and thereby to minimize their total surface area under the restriction of enclosing a given amount of volume. T..