Decomposition of extremal length and a proof of Shen’s conjecture on QED constant and boundary dilatation

Tao Cheng; Shanshuang Yang

doi:10.1007/s00209-014-1353-z

Decomposition of extremal length and a proof of Shen’s conjecture on QED constant and boundary dilatation

Tao Cheng^*
, Shanshuang Yang

^*此作品的通讯作者

数学科学学院

Emory University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

In this paper we study the relations among various constants of quasiextremal distance (QED) domains in the plane. In particular, we give an affirmative answer to Shen’s conjecture about the relation between the QED constant (Ω)and the boundary dilatation(Ω).This leads to the conclusion that, for a large class of domains, the equality M(Ω)1Ω conjectured by Garnett and Yang does not hold, where Ω is the quasiconformal reflection constant.

源语言	英语
页（从-至）	1195-1211
页数	17
期刊	Mathematische Zeitschrift
卷	278
期	3-4
DOI	https://doi.org/10.1007/s00209-014-1353-z
出版状态	已出版 - 12 11月 2014

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abstract = "In this paper we study the relations among various constants of quasiextremal distance (QED) domains in the plane. In particular, we give an affirmative answer to Shen{\textquoteright}s conjecture about the relation between the QED constant (Ω)and the boundary dilatation(Ω).This leads to the conclusion that, for a large class of domains, the equality M(Ω)1Ω conjectured by Garnett and Yang does not hold, where Ω is the quasiconformal reflection constant.",

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AU - Cheng, Tao

AU - Yang, Shanshuang

PY - 2014/11/12

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N2 - In this paper we study the relations among various constants of quasiextremal distance (QED) domains in the plane. In particular, we give an affirmative answer to Shen’s conjecture about the relation between the QED constant (Ω)and the boundary dilatation(Ω).This leads to the conclusion that, for a large class of domains, the equality M(Ω)1Ω conjectured by Garnett and Yang does not hold, where Ω is the quasiconformal reflection constant.

AB - In this paper we study the relations among various constants of quasiextremal distance (QED) domains in the plane. In particular, we give an affirmative answer to Shen’s conjecture about the relation between the QED constant (Ω)and the boundary dilatation(Ω).This leads to the conclusion that, for a large class of domains, the equality M(Ω)1Ω conjectured by Garnett and Yang does not hold, where Ω is the quasiconformal reflection constant.

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KW - 30C70

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ER -

Decomposition of extremal length and a proof of Shen’s conjecture on QED constant and boundary dilatation

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