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A Note on Polyharmonic Mappings

A Note on Polyharmonic Mappings 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00406-4
Publisher site
See Article on Publisher Site

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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Sep 1, 2022

Keywords: Polyharmonic mappings; Biharmonic mappings; Harmonic mappings; Radó theorem; Boundary extensions; Close-to-convex mappings; Primary 30D60; 30C45; Secondary 31A30

References