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A new method to construct polynomial minimal surfaces

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Abstract

Minimal surface is an important type of surface with zero mean curvature. It exists widely in nature. The problem of finding all minimal surfaces presented in parametric form as polynomials is discussed by many authors. However, most of the constructions are based on the theorem that a harmonic surface with isothermal parameterization is minimal. As we all know, Weierstrass representation is a classical parameterization of minimal surfaces. Therefore, in this paper, we consider to construct polynomial minimal surfaces of arbitrary degree by Weierstrass representation. Moreover, there is a correspondence between our constructed polynomial minimal surfaces and Pythagorean hodograph curves. Several numerical examples are demonstrated to illustrate our results.

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Authors and Affiliations

  1. Faculty of Science, Jiangsu University, Zhenjiang, China

    Yong-Xia Hao

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  1. Yong-Xia Hao
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Correspondence to Yong-Xia Hao.

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Communicated by Andreas Fischer.

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This work was supported by the National Natural Science Foundation of China (No. 11801225), University Science Research Project of Jiangsu Province (No. 18KJB110005) and the Research Foundation for Advanced Talents of Jiangsu University (No. 14JDG034).

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Hao, YX. A new method to construct polynomial minimal surfaces. Comp. Appl. Math. 39, 275 (2020). https://doi.org/10.1007/s40314-020-01324-2

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  • DOI: https://doi.org/10.1007/s40314-020-01324-2

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