On the construction of polynomial minimal surfaces with Pythagorean normals
作者：
Highlights：
• A novel approach to constructing polynomial minimal surfaces is presented.
• Minimal surfaces arise from Pythagorean triples of complex polynomials.
• They are Pythagorean-normal surfaces with isothermal parameterization.
• Generalization to minimal surfaces in non-isothermal parameterization is given.
• Cubic, quartic and quintic examples are presented and visualized.
摘要
•A novel approach to constructing polynomial minimal surfaces is presented.•Minimal surfaces arise from Pythagorean triples of complex polynomials.•They are Pythagorean-normal surfaces with isothermal parameterization.•Generalization to minimal surfaces in non-isothermal parameterization is given.•Cubic, quartic and quintic examples are presented and visualized.
论文关键词：Pythagorean–hodograph curves,Pythagorean–normal surfaces,Minimal surfaces,Enneper–Weierstrass parameterization,Plateau’s problem,Quaternions
论文评审过程：Received 4 March 2022, Revised 29 June 2022, Accepted 21 July 2022, Available online 8 August 2022, Version of Record 5 September 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127439
