Sewing homeomorphism and conformal invariants

Tao Cheng; Hui Qiang Shi; Shanshuang Yang

doi:10.1007/s10114-017-6481-z

Sewing homeomorphism and conformal invariants

Tao Cheng, Hui Qiang Shi, Shanshuang Yang

School of Mathematical Sciences

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

1 Scopus citations

Abstract

This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.

Original language	English
Pages (from-to)	1321-1338
Number of pages	18
Journal	Acta Mathematica Sinica, English Series
Volume	33
Issue number	10
DOIs	https://doi.org/10.1007/s10114-017-6481-z
State	Published - 1 Oct 2017

Keywords

Bi-Lipschitz
bi-Hölder
modulus
quasicircle
reduced extremal distance

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10.1007/s10114-017-6481-z

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author = "Tao Cheng and Shi, \{Hui Qiang\} and Shanshuang Yang",

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AU - Shi, Hui Qiang

AU - Yang, Shanshuang

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N2 - This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.

AB - This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.

KW - Bi-Lipschitz

KW - bi-Hölder

KW - modulus

KW - quasicircle

KW - reduced extremal distance

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DO - 10.1007/s10114-017-6481-z

M3 - 文章

AN - SCOPUS:85029808375

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 10

ER -

Sewing homeomorphism and conformal invariants

Abstract

Keywords

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