Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Download PDF
21 pages

Loading next page...
 
/lp/springer-journals/close-to-harmonic-extensions-on-the-plane-44OCaPXUyz
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 Mathematik – Springer Journals

Published: Apr 1, 2022

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

References

  • Quasiconformal extension of meromorphic functions with nonzero pole
    Bhowmik, B; Satpati, G; Sugawa, T
  • Quasiconformal extensions for some geometric subclasses of univalent functions
    Brown, JE
  • Quasiconformal extensions of harmonic mappings with a complex parameter
    Chen, X; Que, Y
  • The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions
    Chuaqui, M; Osgood, B
  • Explicit quasiconformal extensions of planar harmonic mappings
    Ganczar, A
  • Chordal Loewner chains with quasiconformal extensions
    Gumenyuk, P; Hotta, I
  • Univalent functions with quasiconformal extensions: Becker’s class and estimates of the third coefficient
    Gumenyuk, P; Hotta, I
  • Quasiconformal extensions of starlike harmonic mappings in the unit disc
    Hamada, H; Honda, T; Shon, KH
  • Loewner chains and quasiconformal extension of holomorphic mappings
    Hamada, H; Kohr, G
  • Univalence criterion and quasiconformal extension of holomorphic mappings
    Hamada, H; Kohr, G
  • Harmonic extensions of quasiconformal maps to hyperbolic space
    Hardt, R; Wolf, M
  • Quasiconformal extension of harmonic mappings in the plane
    Hernández, R; Martín, MJ
  • Stable geometric properties of analytic and harmonic functions
    Hernández, R; Martín, MJ
  • Harmonic quasiconformal mappings on the upper half-plane
    Huang, X
  • Boundary correspondence under quasiconformal harmonic diffeomorphisms of a half-plane
    Kalaj, D; Pavlović, M
  • Grunsky inequalities and quasiconformal extension
    Krushkal, S; Kühnau, R
  • On the non-vanishing of the Jacobian in certain one-to-one mappings
    Lewy, H
  • Dilatation function of the Beurling-Ahlfors extension
    Long, B; Huang, X
  • Quasiconformality of harmonic mappings between Jordan domains
    Mateljević, M; Božin, V; Knežević, M
  • Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself
    Michalski, A
  • Boundary correspondence under harmonic quasiconformal homeomorphisms of the unit disk
    Pavlović, M
  • Some estimates for harmonic mappings with given boundary function
    Zhu, J