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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Les auteurs sont reconnaissants au CNPq-BRASIL pour son soutien financier
Le second auteur souhaite remercier la P.U.C. de Rio de Janeiro pour son hospitalité durant la préparation de ce travail
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Earp, R.S., Toubiana, E. Sur les surfaces de Weingarten spéciales de type minimal. Bol. Soc. Bras. Mat 26, 129–148 (1995). https://doi.org/10.1007/BF01236989
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DOI: https://doi.org/10.1007/BF01236989