关于$n$ -空间中拟共形映射的Mori定理
On Mori's theorem for quasiconformal maps in the $n$-space
摘要：
R. Fehlmann和M. Vuorinen在1988年证明，森的常数$M(n,K)$的$K$ -拟共形映射的单位球在$\mathbf{R}^n$到本身保持原点固定满足$M(n,K) \to 1$时，$K\to 1 .$我们在这里给这一事实的另一种证明，与定量上限的常数方面的初等函数。我们的证明是基于一个改进的方法，由于G. D。Anderson和M. K. Vamanamurthy。我们还给出了单位圆盘拟共形自映射的Schwarz引理的一个显式版本。提供了一些实验结果来比较当$n=2 .$
英文摘要：
R. Fehlmann and M. Vuorinen proved in 1988 that Mori's constant $M(n,K)$ for $K$-quasiconformal maps of the unit ball in $\mathbf{R}^n$ onto itself keeping the origin fixed satisfies $M(n,K) \to 1$ when $K\to 1 .$ We give here an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M. K. Vamanamurthy. We also give an explicit version of the Schwarz lemma for quasiconformal self-maps of the unit disk. Some experimental results are provided to compare the various bounds for the Mori constant when $n=2 .$
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