Sur les surfaces de Weingarten spéciales de type minimal

  • Ricardo Sa Earp
  • Eric Toubiana
Article
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Abstract

We derive a classification of special Weingarten rotation surfaces of minimal type in Euclidean space. We prove existence and uniqueness, and we give a necessary and sufficient condition to have a complete surface. Futhermore, we prove that under some further simple condition there is a 1- parameter family of complete special surfaces with the same geometrical behaviour as the minimal catenoids family. We remark that there is in our context of special Weingarten minimal type surfaces related “half space theorem”, of Hoffman and Meeks, and “Bernstein theorem”.

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Copyright information

© Sociedade Brasileira de Matemática 1995

Authors and Affiliations

  • Ricardo Sa Earp
    • 1
  • Eric Toubiana
    • 2
  1. 1.Departamento de MatemáticaPontifícia Universidade CatólicaRio de JaneiroBresil
  2. 2.Département de MathématiquesUniversité Paris VIIPARIS-Cedex 05France

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