INJECTIVITY CRITERIA OF LINEAR COMBINATIONS OF HARMONIC QUASIREGULAR MAPPINGS

Jie Huang; Antti Rasila; Jian Feng Zhu

doi:10.2996/kmj47104

INJECTIVITY CRITERIA OF LINEAR COMBINATIONS OF HARMONIC QUASIREGULAR MAPPINGS

Jie Huang, Antti Rasila^*, Jian Feng Zhu

^*Corresponding author for this work

Mathematics with Computer Science

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

Abstract

In this paper, we consider linear combinations of harmonic K-quasiregular mappings f_j = h_j + g_j (j = 1; 2) of the class Har(k; ϕ_j), where k ∈ [0; 1), kω_fj k_∞ = kgj^0=hj^0k∞^{≤ k < 1, k =(1 K)=(1 + K), and ϕ} j = h_j + e^iθg_j is a univalent analytic function. We provide su‰cient conditions for the linear combinations of mappings in these classes to be univalent and for the image domains to be linearly connected. Furthermore, we consider under which conditions the linear combination f is bi-Lipschitz.

Original language	English
Pages (from-to)	52-66
Number of pages	15
Journal	Kodai Mathematical Journal
Volume	47
Issue number	1
DOIs	https://doi.org/10.2996/kmj47104
State	Published - 2024

Keywords

Harmonic mappings
Lipschitz continuity
linear combinations
linear connectedness
quasiconformal mappings

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title = "INJECTIVITY CRITERIA OF LINEAR COMBINATIONS OF HARMONIC QUASIREGULAR MAPPINGS",

abstract = "In this paper, we consider linear combinations of harmonic K-quasiregular mappings fj = hj + gj (j = 1; 2) of the class Har(k; ϕj), where k ∈ [0; 1), kωfj k∞ = kgj0=hj0k∞≤ k < 1, k =(1 K)=(1 + K), and ϕ j = hj + eiθgj is a univalent analytic function. We provide su‰cient conditions for the linear combinations of mappings in these classes to be univalent and for the image domains to be linearly connected. Furthermore, we consider under which conditions the linear combination f is bi-Lipschitz.",

keywords = "Harmonic mappings, Lipschitz continuity, linear combinations, linear connectedness, quasiconformal mappings",

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

year = "2024",

doi = "10.2996/kmj47104",

language = "英语",

volume = "47",

pages = "52--66",

journal = "Kodai Mathematical Journal",

issn = "0386-5991",

publisher = "Tokyo Institute of Technology",

number = "1",

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TY - JOUR

T1 - INJECTIVITY CRITERIA OF LINEAR COMBINATIONS OF HARMONIC QUASIREGULAR MAPPINGS

AU - Huang, Jie

AU - Rasila, Antti

AU - Zhu, Jian Feng

PY - 2024

Y1 - 2024

N2 - In this paper, we consider linear combinations of harmonic K-quasiregular mappings fj = hj + gj (j = 1; 2) of the class Har(k; ϕj), where k ∈ [0; 1), kωfj k∞ = kgj0=hj0k∞≤ k < 1, k =(1 K)=(1 + K), and ϕ j = hj + eiθgj is a univalent analytic function. We provide su‰cient conditions for the linear combinations of mappings in these classes to be univalent and for the image domains to be linearly connected. Furthermore, we consider under which conditions the linear combination f is bi-Lipschitz.

AB - In this paper, we consider linear combinations of harmonic K-quasiregular mappings fj = hj + gj (j = 1; 2) of the class Har(k; ϕj), where k ∈ [0; 1), kωfj k∞ = kgj0=hj0k∞≤ k < 1, k =(1 K)=(1 + K), and ϕ j = hj + eiθgj is a univalent analytic function. We provide su‰cient conditions for the linear combinations of mappings in these classes to be univalent and for the image domains to be linearly connected. Furthermore, we consider under which conditions the linear combination f is bi-Lipschitz.

KW - Harmonic mappings

KW - Lipschitz continuity

KW - linear combinations

KW - linear connectedness

KW - quasiconformal mappings

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U2 - 10.2996/kmj47104

DO - 10.2996/kmj47104

M3 - 文章

AN - SCOPUS:85187871720

SN - 0386-5991

VL - 47

SP - 52

EP - 66

JO - Kodai Mathematical Journal

JF - Kodai Mathematical Journal

IS - 1

ER -

INJECTIVITY CRITERIA OF LINEAR COMBINATIONS OF HARMONIC QUASIREGULAR MAPPINGS

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