A Weierstrass Representation Formula for Discrete Harmonic Surfaces
Differential Geometry
2024-04-18 v3
Abstract
A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformations. Given a topological trivalent graph, a holomorphic function, and an associated discrete holomorphic quadratic form, a version of the Weierstrass representation formula for discrete harmonic surfaces in the 3-dimensional Euclidean space is proposed. By using the formula, a smooth converging sequence of discrete harmonic surfaces is constructed, and its limit is a classical minimal surface defined with the same holomorphic data. As an application, we have a discrete approximation of the Enneper surface.
Keywords
Cite
@article{arxiv.2307.08537,
title = {A Weierstrass Representation Formula for Discrete Harmonic Surfaces},
author = {Motoko Kotani and Hisashi Naito},
journal= {arXiv preprint arXiv:2307.08537},
year = {2024}
}