Koebe and Caratheódory type boundary behavior results for harmonic mappings

Daoud Bshouty; Jiaolong Chen; Stavros Evdoridis; Antti Rasila

doi:10.1080/17476933.2020.1851212

Koebe and Caratheódory type boundary behavior results for harmonic mappings

Daoud Bshouty, Jiaolong Chen, Stavros Evdoridis, Antti Rasila^*

^*Corresponding author for this work

Mathematics with Computer Science

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

2 Scopus citations

Abstract

We study the behavior of the boundary function of a harmonic mapping from global and local points of view. Results related to the Koebe lemma are proved, as well as a generalization of a boundary behavior theorem by Bshouty, Lyzzaik and Weitsman. We also discuss this result from a different point of view, from which a relation between the boundary behavior of the dilatation at a boundary point and the continuity of the boundary function of our mapping can be seen.

Original language	English
Pages (from-to)	962-974
Number of pages	13
Journal	Complex Variables and Elliptic Equations
Volume	67
Issue number	4
DOIs	https://doi.org/10.1080/17476933.2020.1851212
State	Published - 2022

Keywords

31A05
Harmonic mapping
Primary: 30C55
Secondary:30C62
boundary behavior

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10.1080/17476933.2020.1851212

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abstract = "We study the behavior of the boundary function of a harmonic mapping from global and local points of view. Results related to the Koebe lemma are proved, as well as a generalization of a boundary behavior theorem by Bshouty, Lyzzaik and Weitsman. We also discuss this result from a different point of view, from which a relation between the boundary behavior of the dilatation at a boundary point and the continuity of the boundary function of our mapping can be seen.",

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author = "Daoud Bshouty and Jiaolong Chen and Stavros Evdoridis and Antti Rasila",

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AU - Bshouty, Daoud

AU - Chen, Jiaolong

AU - Evdoridis, Stavros

AU - Rasila, Antti

PY - 2022

Y1 - 2022

N2 - We study the behavior of the boundary function of a harmonic mapping from global and local points of view. Results related to the Koebe lemma are proved, as well as a generalization of a boundary behavior theorem by Bshouty, Lyzzaik and Weitsman. We also discuss this result from a different point of view, from which a relation between the boundary behavior of the dilatation at a boundary point and the continuity of the boundary function of our mapping can be seen.

AB - We study the behavior of the boundary function of a harmonic mapping from global and local points of view. Results related to the Koebe lemma are proved, as well as a generalization of a boundary behavior theorem by Bshouty, Lyzzaik and Weitsman. We also discuss this result from a different point of view, from which a relation between the boundary behavior of the dilatation at a boundary point and the continuity of the boundary function of our mapping can be seen.

KW - 31A05

KW - Harmonic mapping

KW - Primary: 30C55

KW - Secondary:30C62

KW - boundary behavior

UR - http://www.scopus.com/inward/record.url?scp=85097592803&partnerID=8YFLogxK

U2 - 10.1080/17476933.2020.1851212

DO - 10.1080/17476933.2020.1851212

M3 - 文章

AN - SCOPUS:85097592803

SN - 1747-6933

VL - 67

SP - 962

EP - 974

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 4

ER -

Koebe and Caratheódory type boundary behavior results for harmonic mappings

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Keywords

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