Conformally invariant complete metrics
In: Mathematical Proceedings of the Cambridge Philosophical Society, 2022; (2020)
Online
report
Zugriff:
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 $\mu_G$ 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 $\mu_G$ admits a minorant in terms of a M\"obius invariant metric. Several applications to quasiconformal maps are given.
Comment: 28 pages
Titel: |
Conformally invariant complete metrics
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Autor/in / Beteiligte Person: | Sugawa, Toshiyuki ; Vuorinen, Matti ; Zhang, Tanran |
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Quelle: | Mathematical Proceedings of the Cambridge Philosophical Society, 2022; (2020) |
Veröffentlichung: | 2020 |
Medientyp: | report |
DOI: | 10.1017/S030500412200024X |
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