# Radó–Kneser–Choquet theorem for harmonic mappings between surfaces

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### Article Info

DATE

2017-01-03

AUTHORS ABSTRACT

We simplify and improve a recent result of Martin (Trans AMS 368:647–658, 2016). Then we prove that if f is an orientation preserving harmonic mapping of the unit disk onto a C3,α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{3,\alpha }$$\end{document} surface Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma$$\end{document} bounded by a Jordan curve γ∈C3,α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \in C^{3,\alpha }$$\end{document}, that belongs to the boundary of a convex domain in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {R}^3$$\end{document}, then f is a diffeomorphism. More... »

PAGES

4

### References to SciGraph publications

• 2010. Minimal Surfaces in NONE
• 2011-11-09. Quasiconformal harmonic mappings between Euclidean surfaces in MONATSHEFTE FÜR MATHEMATIK
• 1956-12. On certain nonlinear elliptic differential equations and univalent mappings in JOURNAL D'ANALYSE MATHÉMATIQUE
• 1978-10. On univalent harmonic maps between surfaces in INVENTIONES MATHEMATICAE
• 2013-11-08. Energy-minimal diffeomorphisms between doubly connected Riemann surfaces in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
• 1984. Harmonic Maps Between Surfaces (with a Special Chapter on Conformal Mappings) in NONE
• 2010-03-31. On Quasiconformal Harmonic Surfaces with Rectifiable Boundary in COMPLEX ANALYSIS AND OPERATOR THEORY
• 1968-04. Über das Nichtverschwinden der Funktionaldeterminante bei einer Klasse eineindeutiger Abbildungen in MATHEMATISCHE ZEITSCHRIFT
• 2014-07-16. The Schwarz Type Inequality for Harmonic Mappings of the Unit Disc with Boundary Normalization in COMPLEX ANALYSIS AND OPERATOR THEORY
• 1973. Quasiconformal Mappings in the Plane in NONE
• 2001-06. Univalent σ-Harmonic Mappings in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
• 1910-03. Sur la généralisation du problème de Dirichlet in MATHEMATISCHE ANNALEN
• 2014-02-19. Heinz Type Inequalities for Poisson Integrals in COMPUTATIONAL METHODS AND FUNCTION THEORY

### Identifiers

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http://scigraph.springernature.com/pub.10.1007/s00526-016-1098-0

DOI

http://dx.doi.org/10.1007/s00526-016-1098-0

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https://app.dimensions.ai/details/publication/pub.1024830766

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