Discrete $\Omega$-nets and Guichard nets via discrete Koenigs nets

TL;DR

This paper presents a discretization of Demoulin's -surfaces, including Guichard and isothermic surfaces, preserving their integrable structure for applications in discrete differential geometry.

Contribution

It introduces a novel discretization method for -surfaces and their specializations, maintaining their integrability properties.

Findings

Successful discretization of Demoulin's -surfaces

Preservation of integrable structure in discrete models

Extension to Guichard and isothermic surfaces

Abstract

We provide a convincing discretisation of Demoulin's $\Omega$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.