Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids

Abstract

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.

References in corpus (1)

• Discrete constant mean curvature surfaces via conserved quantities

Cited by in corpus (2)

• Semi-discrete isothermic surfaces
• Semi-discrete linear Weingarten surfaces with Weierstrass-type representations and their singularities