Asymptotic conformality of the Barycentric extension of quasiconformal maps

Katsuhiko Matsuzaki, Masahiro Yanagishita

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    3 Citations (Scopus)

    Abstract

    We first remark that the complex dilatation of a quasiconformal homeomorphism of a hyperbolic Riemann surface R obtained by the barycentric extension due to Douady-Earle vanishes at any cusp of R. Then we give a new proof, without using the Bers embedding, of a fact that the quasiconformal homeomorphism obtained by the barycentric extension from an integrable Beltrami coefficient on R is asymptotically conformal if R satisfies a certain geometric condition.

    Original languageEnglish
    Pages (from-to)85-90
    Number of pages6
    JournalFilomat
    Volume31
    Issue number1
    DOIs
    Publication statusPublished - 2017

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    Keywords

    • Asymptotically conformal
    • Barycentric extension
    • Bers embedding
    • Complex dilatation
    • Integrable teichmüller space
    • Quasiconformal
    • Teichmüller projection

    ASJC Scopus subject areas

    • Mathematics(all)

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