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,...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212161 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Weierstrass Representation Formula for Discrete Harmonic Surfaces. Motoko Kotani and Hisashi Naito. SIGMA 20 (2024), 034, 15 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 |