Access the full text.
Sign up today, get DeepDyve free for 14 days.
W. Hengartner, G. Schober (1986)
Harmonic Mappings with Given DilatationJournal of The London Mathematical Society-second Series
W. Langlois, M. Deville (1964)
Slow viscous flow
T. Radó (1926)
Über den analytischen Charakter der MinimalflächenMathematische Zeitschrift, 24
Jiaolong Chen, A. Rasila, Xiantao Wang (2013)
Landau’s theorem for polyharmonic mappings ☆Journal of Mathematical Analysis and Applications, 409
J. Clunie, T. Sheil‐Small (1984)
Harmonic univalent functions, 9
O. Lossers (1975)
Lösung der Aufgabe 741Elemente Der Mathematik, 31
Saminathan Ponnysamy, A. Rasila (2013)
Planar Harmonic and Quasiregular Mappings
Sh. Chen, S. Ponnusamy, Xiantao Wang (2011)
Bloch constant and Landau's theorem for planar p-harmonic mappingsJournal of Mathematical Analysis and Applications, 373
Jiaolong Chen, A. Rasila, Xiantao Wang (2013)
Starlikeness and convexity of polyharmonic mappingsBulletin of The Belgian Mathematical Society-simon Stevin, 21
P Duren (2004)
10.1017/CBO9780511546600Harmonic mappings in the plane
S. Khuri (1996)
Biorthogonal Series Solution of Stokes Flow Problems in Sectorial RegionsSIAM J. Appl. Math., 56
J. Qiao, Xiantao Wang (2012)
Subordination of $p$-harmonic mappingsBulletin of The Belgian Mathematical Society-simon Stevin, 19
D. Bshouty, A. Lyzzaik (2014)
Boundary Behavior of Univalent Harmonic Mappings
J. Nitsche (1958)
On harmonic mappings, 9
Jiaolong Chen, A. Rasila, Xiantao Wang (2014)
ON LENGTHS, AREAS AND LIPSCHITZ CONTINUITY OF POLYHARMONIC MAPPINGSJournal of Mathematical Analysis and Applications, 422
P. Duren (2004)
Harmonic Mappings in the Plane
(1945)
Sur un type de transformation analytique généralisant la représentation conforme et définie au moyen de fonctions harmoniques, Bull. Sco
D. Armitage (1984)
POLYHARMONIC FUNCTIONS (Oxford Mathematical Monographs)Bulletin of The London Mathematical Society, 16
Jiaolong Chen, A. Rasila, Xiantao Wang (2013)
ON POLYHARMONIC UNIVALENT MAPPINGSMathematical Reports, 15
J. Happel, H. Brenner (1973)
Low Reynolds number hydrodynamics: with special applications to particulate media
J. Chen, A. Rasila, Xiantao Wang (2015)
Coefficient estimates and radii problems for certain classes of polyharmonic mappingsComplex Variables and Elliptic Equations, 60
J Chen, A Rasila, X Wang (2015)
Coefficient estimates and radii problems for certain classes of polyharmonic mappings, to appear in complex varElliptic Equ., 60
D. Bshouty, Jiaolong Chen, Stavros Evdoridis, A. Rasila (2020)
Koebe and Caratheódory type boundary behavior results for harmonic mappingsComplex Variables and Elliptic Equations, 67
L. Bers (1951)
Isolated Singularities of Minimal SurfacesAnnals of Mathematics, 53
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
D. Bshouty, A. Lyzzaik, Allen Weitsman (2012)
ON THE BOUNDARY BEHAVIOUR OF UNIVALENT HARMONIC MAPPINGSAnnales Academiae Scientiarum Fennicae. Mathematica, 37
J. Jahangiri, H. Silverman (2002)
Harmonic close-to-convex mappings.Journal of Applied Mathematics and Stochastic Analysis, 15
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.
Computational Methods and Function Theory – Springer 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
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.