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Close-to-harmonic extensions on the plane

Close-to-harmonic extensions on the plane In this paper, some explicit harmonic homeomorphic extensions are constructed. Necessary and sufficient conditions are obtained for the harmonic extensions to be quasiconformal. The extensions considered include those from the unit circle (or real axis) to the unit disk (or upper half plane) and from the unit disk (or upper half plane) to the whole plane. Furthermore, a new concept called close-to-harmonic extension is introduced and several open problems are proposed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monatshefte für Mathematik Springer Journals

Close-to-harmonic extensions on the plane

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2022
ISSN
0026-9255
eISSN
1436-5081
DOI
10.1007/s00605-022-01668-3
Publisher site
See Article on Publisher Site

Abstract

In this paper, some explicit harmonic homeomorphic extensions are constructed. Necessary and sufficient conditions are obtained for the harmonic extensions to be quasiconformal. The extensions considered include those from the unit circle (or real axis) to the unit disk (or upper half plane) and from the unit disk (or upper half plane) to the whole plane. Furthermore, a new concept called close-to-harmonic extension is introduced and several open problems are proposed.

Journal

Monatshefte für MathematikSpringer Journals

Published: Apr 1, 2022

Keywords: Extension; Harmonic mapping; Quasiconformal mapping; Homeomorphism; 31A05; 30C62

References