In this paper, we first establish a degeneracy second main theorem for algebraic curves from compact complex Riemann surfaces into projective varieties intersecting hypersurfaces in subgeneral position. We then use it to study the ramified values for the Gauss map of the complete (regular) minimal surfaces in ℝm with finite total curvature in the case where the Gauss map may be algebraic degenerate. Our results generalize and improve the previous results in the field.

中文翻译：

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代数曲线的分布值和代数极小曲面上的高斯图

在本文中，我们首先建立了从紧复黎曼曲面到在次一般位置相交超曲面的射影簇的代数曲线的简并第二主定理。然后我们用它来研究完整（规则）最小表面的高斯图的分枝值ℝ米在高斯图可能是代数退化的情况下，总曲率有限。我们的结果概括并改进了该领域以前的结果。