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A Weierstrass Representation Formula for Discrete Harmonic Surfaces
Motoko Kotania, Hisashi Naitob a The Advanced Institute for Materials Research (AIMR), Tohoku University, Japan
b Graduate School of Mathematics, Nagoya University, Japan
Аннотация:
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.
Ключевые слова:
discrete harmonic surfaces, minimal surfaces, Weierstrass representation formula.
Поступила: 17 июля 2023 г.; в окончательном варианте 12 апреля 2024 г.; опубликована 17 апреля 2024 г.
Образец цитирования:
Motoko Kotani, Hisashi Naito, “A Weierstrass Representation Formula for Discrete Harmonic Surfaces”, SIGMA, 20 (2024), 034, 15 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma2036 https://www.mathnet.ru/rus/sigma/v20/p34
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