有限全曲率完备极小曲面的高斯映射
微分几何
2019-06-24 v3
摘要
在文献[15]中，Robert Osserman 证明了 中具有有限全曲率的完备非平坦极小曲面的高斯映射的像最多遗漏 3 个点。本文我们证明此类极小浸入的高斯映射最多遗漏 2 个点。这是一个精确的结果，因为悬链面的高斯映射恰好遗漏两个点。事实上，我们针对更广泛的一类等距浸入证明了这一结果，这类浸入具有与有限全曲率完备极小曲面相同的基本微分拓扑性质。
引用
@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}
}
备注
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