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The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature

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 in3 with finite total curvature, which is not a plane, omits at most three points of𝕊2

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

Gauss map; minimal surfaces; Finite total curvature; Image of the Gauss map


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