论文标题
Teichmüller关于格罗莫夫双曲线域的问题
Teichmüller's problem for Gromov hyperbolic domains
论文作者
论文摘要
令$ \ mathcal {t} _k（d）$为域的$ k $ - quasiconformal usormormormormormormorphisms $ d \ subsetneq \ subsetneq \ subsetneq \ mathbb {r}^n $，具有身份边界值。 Teichmüller的问题是确定在\ Mathcal {t} _K（d）$的映射$ f \中，可以将给定点$ x \ in D $映射到多远。我们通过使用两个不同的度量标准和quasihyperbolic指标来估计上述$ x $和$ f（x）$之间的距离。我们研究了$ \ mathbb {r}^n $中Gromov双曲线域的Teichmüller问题，其身份值在Infinity的边界处。作为应用程序，我们在$ \ Mathbb {r}^n $中的$ψ$ - 均匀域和内部统一域中获得了Teichmüller的问题。
Let $\mathcal{T}_K(D)$ be the class of $K$-quasiconformal automorphisms of a domain $D\subsetneq \mathbb{R}^n$ with identity boundary values. Teichmüller's problem is to determine how far a given point $x\in D$ can be mapped under a mapping $f\in \mathcal{T}_K(D)$. We estimate this distance between $x$ and $f(x)$ from the above by using two different metrics, the distance ratio metric and the quasihyperbolic metric. We study Teichmüller's problem for Gromov hyperbolic domains in $\mathbb{R}^n$ with identity values at the boundary of infinity. As applications, we obtain results on Teichmüller's problem for $ψ$-uniform domains and inner uniform domains in $\mathbb{R}^n$.
