论文标题
欧几里得空间中最小表面的柔性域
Flexible domains for minimal surfaces in Euclidean spaces
论文作者
论文摘要
在本文中，我们介绍并研究了欧几里得空间中域的灵活性的新概念$ \ mathbb r^n $，以$ n \ ge 3 $在所包含的最小表面方面。如果从runge domain $ u \ u \toΩ$中的每一个$ \ u \toΩ$从runge域中$ u $ u $ y $在一个开放的子状表面$ m $中均匀近似于紧凑型，则在任何给定的有限额的插入式上，由任何给定的有限额度均匀地近似于，由任何给定的有限额近似，由任何给定的有限额近似，由任何给定的有限额近似，由任何给定的有限额近似，由任何给定的有限量近似，由任何给定的有限的$ m minimal minimal rimision $ m m \ y \ for，加上最近著作中考虑的双曲线现象，从复杂分析到最小的表面理论，将二分法扩展到二分法之间。
In this paper we introduce and investigate a new notion of flexibility for domains in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ in terms of minimal surfaces which they contain. A domain $Ω$ in $\mathbb R^n$ is said to be flexible if every conformal minimal immersion $U\toΩ$ from a Runge domain $U$ in an open conformal surface $M$ can be approximated uniformly on compacts, with interpolation on any given finite set, by conformal minimal immersion $M\to Ω$. Together with hyperbolicity phenomena considered in recent works, this extends the dichotomy between flexibility and rigidity from complex analysis to minimal surface theory.
