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A Weierstrass Representation Formula for Discrete Harmonic Surfaces
- Source :
- SIGMA 20 (2024), 034, 15 pages
- Publication Year :
- 2023
-
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.
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Journal :
- SIGMA 20 (2024), 034, 15 pages
- Publication Type :
- Report
- Accession number :
- edsarx.2307.08537
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3842/SIGMA.2024.034