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Immersions of Finite Geometric Type in Euclidean Spaces

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Abstract

In this paper, we introduce the class of hypersurfaces of finitegeometric type. They are defined as the ones that share the basicdifferential topological properties of minimal surfaces of finite totalcurvature. We extend to surfaces in this class the classical theorem ofOsserman on the number of omitted points of the Gauss mapping ofcomplete minimal surfaces of finite total curvature. We give aclassification of the even-dimensional catenoids as the only even-dimensional minimal hypersurfaces of R n of finite geometric type.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, Campus do PICI, 60455-760, Fortaleza, Ce., Brazil

    J. L. M. Barbosa

  2. Departamento de Matemática, Universidade Estadual de Maringá, Av. Colombo 5790, Zona 7, 87020-900, Maringá, P.R., Brazil

    R. Fukuoka

  3. Departamento de Matemática, Universidade Estadual de Campinas, 13081-970, Campinas S.P., Brazil

    F. Mercuri

Authors
  1. J. L. M. Barbosa
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  2. R. Fukuoka
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  3. F. Mercuri
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Barbosa, J.L.M., Fukuoka, R. & Mercuri, F. Immersions of Finite Geometric Type in Euclidean Spaces. Annals of Global Analysis and Geometry 22, 301–315 (2002). https://doi.org/10.1023/A:1020557829900

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  • DOI: https://doi.org/10.1023/A:1020557829900

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