Certain Integrability of Quasisymmetric Automorphisms of the Circle

    Research output: Contribution to journalArticle

    Abstract

    Using the correspondence between the quasisymmetric quotient and the variation of the cross-ratio for a quasisymmetric automorphism (Formula presented.) of the unit circle, we establish a certain integrability of the complex dilatation of a quasiconformal extension of (Formula presented.) to the unit disk if the Liouville cocycle for (Formula presented.) is integrable. Moreover, under this assumption, we verify regularity properties of (Formula presented.) such as being bi-Lipschitz and symmetric.

    Original languageEnglish
    Pages (from-to)487-503
    Number of pages17
    JournalComputational Methods and Function Theory
    Volume14
    Issue number2-3
    DOIs
    Publication statusPublished - 2014 Oct 31

    Fingerprint

    Integrability
    Automorphisms
    Circle
    Cross ratio
    Quasiconformal
    Dilatation
    Regularity Properties
    Cocycle
    Unit circle
    Automorphism
    Unit Disk
    Lipschitz
    Quotient
    Correspondence
    Verify

    Keywords

    • Asymptotically conformal
    • Complex dilatation
    • Cross-ratio
    • Liouville cocycle
    • Quasiconformal map
    • Quasisymmetric quotient

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Computational Theory and Mathematics

    Cite this

    Certain Integrability of Quasisymmetric Automorphisms of the Circle. / Matsuzaki, Katsuhiko.

    In: Computational Methods and Function Theory, Vol. 14, No. 2-3, 31.10.2014, p. 487-503.

    Research output: Contribution to journalArticle

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