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2013•Anais da Academia Brasileira de CiênciasOpen access

The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature

Pedro A. Hinojosa, GILVANEIDE N. SILVA

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Abstract

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 in ℝ3 with 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.

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What this paper is about

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 in ℝ3 with 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.

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Available abstract

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 in ℝ3 with 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.

Key concepts: Total curvature, Gauss map, Gaussian curvature, Curvature, Gauss, Minimal surface, Mathematics, Constant-mean-curvature surface

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