Conformally invariant complete metrics

被引：4

作者：

Sugawa, Toshiyuki ^{[1
]}

Vuorinen, Matti ^{[2
]}

Zhang, Tanran ^{[3
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Aoba ku, Sendai 9808579, Japan

[2] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

[3] Soochow Univ, Dept Math, 1 Shizi St, Suzhou 215006, Peoples R China

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2023年 / 174卷 / 02期

关键词：

30C35; 30C55; UNIFORMLY PERFECT SETS; CAPACITIES; DOMAINS;

D O I：

10.1017/S030500412200024X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a domain Gin the one-point compactification R-n = R-n boolean OR {infinity} of R-n, n? 2, we characterise the completeness of the modulus metric mu(G )in terms of a potential-theoretic thickness condition of 8G, Martio's M-condition [35]. Next, we prove that 8G is uniformly perfect if and only if mu(G) admits a minorant in terms of a Mobius invariant metric. Several applications to quasiconformal maps are given.

引用

页码：273 / 300

页数：28

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