Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids. (English) Zbl 1302.53014
Summary: 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.
MSC:
53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |