Abstract
We consider a family of higher degree Enneper minimal surface E m for positive integers m in the three-dimensional Euclidean space E 3 . We compute algebraic equation, degree and integral free representation of Enneper minimal surface for m = 1 , 2 , 3 . Finally, we give some results and relations for the family E m .
Highlights
Minimal surfaces have an important role in the mathematics, physics, biology, architecture, etc
A minimal surface in E3 is a regular surface for which the mean curvature vanishes identically
We introduce a family of higher degree Enneper minimal surface Em for positive integers m in the three-dimensional Euclidean space E3
Summary
Minimal surfaces have an important role in the mathematics, physics, biology, architecture, etc. We only see a few notable works about algebraic minimal surfaces, including general results and the properties. They were given by Enneper [11,12], Henneberg [13,14] and Weierstrass [9,15]. We give some general findings for a family of higher degree Enneper minimal surface Em with a table in the last section
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