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Anais da Academia Brasileira de Ciências

Print version ISSN 0001-3765

Abstract

HINOJOSA, PEDRO A.  and  SILVA, GILVANEIDE N.. The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature. An. Acad. Bras. Ciênc. [online]. 2013, vol.85, n.4, pp.1217-1226.  Epub Nov 10, 2013. ISSN 0001-3765.  http://dx.doi.org/10.1590/0001-3765201376911.

In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature. We give a different proof of the following theorem of R. Osserman:The normal Gauss map of a minimal surface immersed inℝ3with finite total curvature, which is not a plane, omits at most three points of��2

Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2.

Keywords : Gauss map; minimal surfaces; Finite total curvature; Image of the Gauss map.

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