Weierstrass representations of discrete constant mean curvature surfaces in isotropic space

TL;DR

This paper develops Weierstrass representations for discrete constant mean curvature surfaces in isotropic space, enabling the construction of explicit examples with closed-form parametrizations.

Contribution

It introduces a novel Weierstrass representation for discrete CMC surfaces in isotropic space, facilitating explicit example construction.

Findings

Weierstrass representations for discrete CMC surfaces in isotropic space are established.

Explicit examples with closed-form parametrizations are constructed.

The approach advances discrete differential geometry in isotropic settings.

Abstract

In this paper, we obtain Weierstrass representations for discrete constant mean curvature surfaces in isotropic 3-space, and use this to construct examples with discrete closed-form parametrizations.