论文标题
共同不变的完整指标
Conformally invariant complete metrics
论文作者
论文摘要
对于一个域$ g $，在单点压实中$ \上线{\ mathbb {r}}^n = \ mathbb {r}^n \ cup \ {\ cup \ {\ infty \} $ of $ \ mathbb {r} $ \ partial g \ ,, $ martio的$ m $ - 条件。接下来，我们证明，只有$μ_g$就Möbius不变式度量允许少数人，$ \ partial g $是统一完美的。给出了准文化图的几个应用。
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.
