The Gauss map of a complete minimal surface with finite total curvature

2016/07/25 by Jorge, Luquesio P., Mercuri, Francesco
#53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.07492

Abstract

In [15] Robert Osserman proved that the image of the Gauss map of a complete, non flat minimal surface in R³ with finite total curvature miss at most 3 points. In this paper we prove that the Gauss map of such a minimal immersions omit at most 2 points. This is a sharp result since the Gauss map of the catenoid omits exactly two points. In fact we prove this result for a wider class of isometric immersions, that share the basic differential topological properties of the complete minimal surfaces of finite total curvature.

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