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

^*此作品的通讯作者

数学科学学院

Emory University
Hunan University of Commerce

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1321-1338
页数	18
期刊	Acta Mathematica Sinica, English Series
卷	33
期	10
DOI	https://doi.org/10.1007/s10114-017-6481-z
出版状态	已出版 - 1 10月 2017

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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-H{\"o}lder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.",

keywords = "Bi-Lipschitz, bi-H{\"o}lder, modulus, quasicircle, reduced extremal distance",

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

note = "Publisher Copyright: {\textcopyright} 2017, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany.",

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T1 - Sewing homeomorphism and conformal invariants

AU - Cheng, Tao

AU - Shi, Hui Qiang

AU - Yang, Shanshuang

PY - 2017/10/1

Y1 - 2017/10/1

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

UR - https://www.scopus.com/pages/publications/85029808375

U2 - 10.1007/s10114-017-6481-z

DO - 10.1007/s10114-017-6481-z

M3 - 文章

AN - SCOPUS:85029808375

SN - 1439-8516

VL - 33

SP - 1321

EP - 1338

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 10

ER -

Sewing homeomorphism and conformal invariants

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