Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part

Jie Huang; Jian Feng Zhu

doi:10.4134/BKMS.b170823

Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part

Jie Huang, Jian Feng Zhu

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

2 Scopus citations

Abstract

Let f = h + g be a harmonic mapping of the unit disk D with the holomorphic part h satisfying that h is injective and h(D) is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

Original language	English
Pages (from-to)	1419-1431
Number of pages	13
Journal	Bulletin of the Korean Mathematical Society
Volume	55
Issue number	5
DOIs	https://doi.org/10.4134/BKMS.b170823
State	Published - 2018
Externally published	Yes

Keywords

Bi-lipschitz mapping
Harmonic mapping
M-linearly connected domain
Quasiconformal mapping

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10.4134/BKMS.b170823

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title = "Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part",

abstract = "Let f = h + g be a harmonic mapping of the unit disk D with the holomorphic part h satisfying that h is injective and h(D) is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.",

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author = "Jie Huang and Zhu, {Jian Feng}",

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AU - Huang, Jie

AU - Zhu, Jian Feng

PY - 2018

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N2 - Let f = h + g be a harmonic mapping of the unit disk D with the holomorphic part h satisfying that h is injective and h(D) is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

AB - Let f = h + g be a harmonic mapping of the unit disk D with the holomorphic part h satisfying that h is injective and h(D) is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

KW - Bi-lipschitz mapping

KW - Harmonic mapping

KW - M-linearly connected domain

KW - Quasiconformal mapping

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M3 - 文章

AN - SCOPUS:85055146063

SN - 1015-8634

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JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 5

ER -

Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part

Abstract

Keywords

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