$R^3$凸体中的完备真极小曲面
Complete proper minimal surfaces in convex bodies of $R^3$
摘要：
考虑空间的一个凸区域B。我们证明了存在完全的极小曲面，它们适当地浸入B中。证明了若D和D'是凸区域，且D有界，D的闭包包含在D'中，则任何以D的边界为边界的极小圆盘，在D的任何紧子域中，都可以用一个在D '中适当的完全极小圆盘来逼近.我们应用这些结果来研究所谓的极小曲面的类型问题：我们证明了任何凸区域的内部不是极小曲面的通用区域，在这个意义上解释的Meeks和Perez。
英文摘要：
Consider a convex domain B of space. We prove that there exist complete minimal surfaces which are properly immersed in B. We also demonstrate that if D and D' are convex domains with D bounded and the closure of D contained in D' then any minimal disk whose boundary lies in the boundary of D, can be approximated in any compact subdomain of D by a complete minimal disk which is proper in D'. We apply these results to study the so called type problem for a minimal surface: we demonstrate that the interior of any convex region is not a universal region for minimal surfaces, in the sense explained by Meeks and Perez.
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