论文标题
Teichmüller的定理在更高的维度及其应用中
Teichmüller's theorem in higher dimensions and its applications
论文作者
论文摘要
对于给定的环（域），$ \叠加{\ mathbb {r}}^n $我们讨论其边界组件是否可以通过模量几乎等于给定环的环形环将其分开。特别是，我们表明，对于所有$ n \ ge 3 \，$，根据欧几里得公制的统一完美集的标准定义等同于分离环模量的界限。我们还建立了一个“一半”戒指的分离定理。作为这些结果的应用，我们将证明球的准文字映射的边界连续性或$ \ mathbb {r}^n。
For a given ring (domain) in $\overline{\mathbb{R}}^n$ we discuss whether its boundary components can be separated by an annular ring with modulus nearly equal to that of the given ring. In particular, we show that, for all $n\ge 3\,,$ the standard definition of uniformly perfect sets in terms of Euclidean metric is equivalent to the boundedness of moduli of separating rings. We also establish separation theorems for a "half" of a ring. As applications of those results, we will prove boundary Hölder continuity of quasiconformal mappings of the ball or the half space in $\mathbb{R}^n.$
