Radó–Kneser–Choquet theorem for harmonic mappings between surfaces View Full Text


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Article Info

DATE

2017-01-03

AUTHORS

David Kalaj

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

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References to SciGraph publications

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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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