A Weierstrass Representation Formula for Discrete Harmonic Surfaces
A discrete harmonic surface is a trivalent graph that satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimization under local deformations. Given a topological trivalent graph, a holomorphic function, and an associated discrete holomorphic quadratic form,...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212161 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Weierstrass Representation Formula for Discrete Harmonic Surfaces. Motoko Kotani and Hisashi Naito. SIGMA 20 (2024), 034, 15 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | A discrete harmonic surface is a trivalent graph that satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimization 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.
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| ISSN: | 1815-0659 |