ISOMETRIES FOR THE MODULUS METRIC ARE QUASICONFORMAL MAPPINGS

被引：5

作者：

Betsakos, Dimitrios ^{[1
]}

Pouliasis, Stamatis ^{[2
]}

机构：

[1] Aristotle Univ Thessaloniki, Dept Math, Thessaloniki 54124, Greece

[2] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 04期

关键词：

Modulus metric; conformal mapping; quasiconformal mapping; condenser capacity; reduced conformal modulus; extremal length; LIPSCHITZ-CONDITIONS; INEQUALITIES;

D O I：

10.1090/tran/7712

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a domain D in R-n, the modulus metric is defined by mu D(x, y) = inf(gamma) cap(D, gamma), where the infimum is taken over all curves gamma in D joining x to y, and "cap" denotes the conformal capacity of the condensers. It has been conjectured by J. Ferrand, G. J. Martin, and M. Vuorinen that isometries in the modulus metric are conformal mappings. We prove the conjecture when n = 2. In higher dimensions, we prove that isometries are quasiconformal mappings.

引用

页码：2735 / 2752

页数：18

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