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 |
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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| _version_ | 1862673622866329600 |
|---|---|
| author | Kotani, Motoko Naito, Hisashi |
| author_facet | Kotani, Motoko Naito, Hisashi |
| citation_txt | A Weierstrass Representation Formula for Discrete Harmonic Surfaces. Motoko Kotani and Hisashi Naito. SIGMA 20 (2024), 034, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-16T18:56:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212161 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T18:56:09Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kotani, Motoko Naito, Hisashi 2026-01-30T08:15:39Z 2024 A Weierstrass Representation Formula for Discrete Harmonic Surfaces. Motoko Kotani and Hisashi Naito. SIGMA 20 (2024), 034, 15 pages 1815-0659 2020 Mathematics Subject Classification: 53A70; 53A10; 52C26 arXiv:2307.08537 https://nasplib.isofts.kiev.ua/handle/123456789/212161 https://doi.org/10.3842/SIGMA.2024.034 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. Motoko Kotani acknowledges the JSPS Grant-in-Aid for Scientific Research (B) under Grant No. JP23H01072. Hisashi Naito acknowledges the JSPS Grant-in-Aid for Scientific Research (C) under Grant No. JP19K03488, No. JP24K06710, and the JSPS Grant-in-Aid for Scientific Research (B) under Grant No. JP23H01072. The authors would like to express their gratitude to the referee for their useful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Weierstrass Representation Formula for Discrete Harmonic Surfaces Article published earlier |
| spellingShingle | A Weierstrass Representation Formula for Discrete Harmonic Surfaces Kotani, Motoko Naito, Hisashi |
| title | A Weierstrass Representation Formula for Discrete Harmonic Surfaces |
| title_full | A Weierstrass Representation Formula for Discrete Harmonic Surfaces |
| title_fullStr | A Weierstrass Representation Formula for Discrete Harmonic Surfaces |
| title_full_unstemmed | A Weierstrass Representation Formula for Discrete Harmonic Surfaces |
| title_short | A Weierstrass Representation Formula for Discrete Harmonic Surfaces |
| title_sort | weierstrass representation formula for discrete harmonic surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212161 |
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