A Note on Polyharmonic Mappings

Daoud Bshouty; Stavros Evdoridis; Antti Rasila

doi:10.1007/s40315-021-00406-4

A Note on Polyharmonic Mappings

Daoud Bshouty, Stavros Evdoridis, Antti Rasila^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Technion - Israel Institute of Technology

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

Abstract

In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic mappings. Finally, we show how a close-to-convex biharmonic mapping can be constructed from a convex harmonic mapping.

Original language	English
Pages (from-to)	433–443
Number of pages	11
Journal	Computational Methods and Function Theory
Volume	22
Early online date	26 Jul 2021
DOIs	https://doi.org/10.1007/s40315-021-00406-4
Publication status	Published - 2022
MoE publication type	A1 Journal article-refereed

Keywords

Biharmonic mappings
Boundary extensions
Close-to-convex mappings
Harmonic mappings
Polyharmonic mappings
Radó theorem

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10.1007/s40315-021-00406-4

Cite this

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title = "A Note on Polyharmonic Mappings",

abstract = "In this paper we prove a Rad{\'o} type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic mappings. Finally, we show how a close-to-convex biharmonic mapping can be constructed from a convex harmonic mapping.",

keywords = "Biharmonic mappings, Boundary extensions, Close-to-convex mappings, Harmonic mappings, Polyharmonic mappings, Rad{\'o} theorem",

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

note = "Funding Information: The research was supported by Academy of Finland (No. 308063), NNSF of China (No. 11971124), NSF of the Guangdong Province (No. 2021A1515010326), and Foundation for Aalto University Science and Technology. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

doi = "10.1007/s40315-021-00406-4",

language = "English",

volume = "22",

pages = "433–443",

journal = "Computational Methods and Function Theory",

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TY - JOUR

T1 - A Note on Polyharmonic Mappings

AU - Bshouty, Daoud

AU - Evdoridis, Stavros

AU - Rasila, Antti

N1 - Funding Information: The research was supported by Academy of Finland (No. 308063), NNSF of China (No. 11971124), NSF of the Guangdong Province (No. 2021A1515010326), and Foundation for Aalto University Science and Technology. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic mappings. Finally, we show how a close-to-convex biharmonic mapping can be constructed from a convex harmonic mapping.

AB - In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic mappings. Finally, we show how a close-to-convex biharmonic mapping can be constructed from a convex harmonic mapping.

KW - Biharmonic mappings

KW - Boundary extensions

KW - Close-to-convex mappings

KW - Harmonic mappings

KW - Polyharmonic mappings

KW - Radó theorem

UR - http://www.scopus.com/inward/record.url?scp=85111161278&partnerID=8YFLogxK

U2 - 10.1007/s40315-021-00406-4

DO - 10.1007/s40315-021-00406-4

M3 - Article

AN - SCOPUS:85111161278

SN - 1617-9447

VL - 22

SP - 433

EP - 443

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

ER -

A Note on Polyharmonic Mappings

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Keywords

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Parabolic flows with variational methods

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A Note on Polyharmonic Mappings

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Parabolic flows with variational methods

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