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Parametric polynomial minimal surfaces of arbitrary degree

Gang Xu 1 Guozhao Wang 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It includes the classical Enneper surface for cubic case. The proposed minimal surfaces also have some interesting properties such as symmetry, containing straight lines and self-intersections. According to the shape properties, the proposed minimal surface can be classified into four categories with respect to $n=4k-1$ $n=4k+1$, $n=4k$ and $n=4k+2$. The explicit parametric form of corresponding conjugate minimal surfaces is given and the isometric deformation is also implemented.
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Submitted on : Monday, August 2, 2010 - 12:07:14 AM
Last modification on : Wednesday, October 26, 2022 - 8:16:46 AM
Long-term archiving on: : Tuesday, October 23, 2012 - 11:56:43 AM


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  • HAL Id : inria-00507790, version 1



Gang Xu, Guozhao Wang. Parametric polynomial minimal surfaces of arbitrary degree. [Research Report] 2010. ⟨inria-00507790⟩



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