The Gauss map of a complete minimal surface with finite total curvature
Abstract
In [15] Robert Osserman proved that the image of the Gauss map of a complete, non flat minimal surface in R^3 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.
Keywords
Cite
@article{arxiv.1607.07492,
title = {The Gauss map of a complete minimal surface with finite total curvature},
author = {Luquesio P. Jorge and Francesco Mercuri},
journal= {arXiv preprint arXiv:1607.07492},
year = {2019}
}
Comments
22 pages. Result about the missing points by the Gauss map of a wide class of complete parabolic surfaces in the 3 dimensional Euclidean space with finite total curvature and the Gauss map extending continuously to a compact Riemann surfaces including the minimal surfaces. If it is no flat then the Gauss map can not miss more than 2 points of the sphere