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

^*Corresponding author for this work

School of Mathematical Sciences

Emory University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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’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.

Original language	English
Pages (from-to)	1195-1211
Number of pages	17
Journal	Mathematische Zeitschrift
Volume	278
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-014-1353-z
State	Published - 12 Nov 2014

Keywords

30C62
30C70

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10.1007/s00209-014-1353-z

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title = "Decomposition of extremal length and a proof of Shen{\textquoteright}s conjecture on QED constant and boundary dilatation",

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

Y1 - 2014/11/12

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.

KW - 30C62

KW - 30C70

UR - https://www.scopus.com/pages/publications/84911970471

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M3 - 文章

AN - SCOPUS:84911970471

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

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

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