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

Mathematics with Computer Science

Research output: Contribution to journal › Article › 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
Issue number	3
DOIs	https://doi.org/10.1007/s40315-021-00406-4
State	Published - Sep 2022

Keywords

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

Access to Document

10.1007/s40315-021-00406-4

Cite this

@article{996d7775ade94c61a49befa59ab539a1,

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 = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

month = sep,

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

language = "英语",

volume = "22",

pages = "433--443",

journal = "Computational Methods and Function Theory",

issn = "1617-9447",

publisher = "Springer Verlag",

number = "3",

}

TY - JOUR

T1 - A Note on Polyharmonic Mappings

AU - Bshouty, Daoud

AU - Evdoridis, Stavros

AU - Rasila, Antti

PY - 2022/9

Y1 - 2022/9

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 - 文章

AN - SCOPUS:85111161278

SN - 1617-9447

VL - 22

SP - 433

EP - 443

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

IS - 3

ER -

A Note on Polyharmonic Mappings

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this