共形不变完备度量
Conformally invariant complete metrics
摘要：
对于$\mathbb{R}^n, n \ge 2$的一点紧化$\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$中的域$G$，我们用$\partial G\,,$ Martio的$M$ -条件的势理论厚度条件刻画了模度量$μ_G$的完备性.其次，我们证明了$\partial G$是一致完美的当且仅当$μ_G$允许一个关于莫比乌斯不变度量的次量.给出了拟共形映射的几个应用。
英文摘要：
For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize the completeness of the modulus metric $μ_G$ in terms of a potential-theoretic thickness condition of $\partial G\,,$ Martio's $M$-condition. Next, we prove that $\partial G$ is uniformly perfect if and only if $μ_G$ admits a minorant in terms of a Möbius invariant metric. Several applications to quasiconformal maps are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
