Weierstrass representation for semi-discrete minimal surfaces, and   comparison of various discretized catenoids
  We give a Weierstrass type representation for semi-discrete minimal surfaces in Euclidean 3-space. We then give explicit parametrizations of various smooth, semi-discrete and fully-discrete catenoids, determined from either variational or integrable systems principles. Finally, we state the shared properties that those various catenoids have. 
Wayne Rossman, Masashi Yasumoto
math.DG