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Enneper immersions

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Abstract

We describe a method to construct minimal surfaces inR 3 which has many computational simplicities and prove that any immersed minimal surface inR 3 may be constructed by using that method. We also show that under certain finite hypotheses on the orders of the coordinate functions, among all conformal minimal immersions of the plane with Gauss mapg=e az+b only the parametrizations of helicoids and planes are proper embeddings.

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Authors and Affiliations

  1. Centro de Ciências Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici Bloco 914, CEP 60.455-760, Fortaleza, CE, Brazil

    Plácido Andrade

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  1. Plácido Andrade
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Correspondence to Plácido Andrade.

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Andrade, P. Enneper immersions. J. Anal. Math. 75, 121–134 (1998). https://doi.org/10.1007/BF02788695

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  • DOI: https://doi.org/10.1007/BF02788695

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