Certain Integrability of Quasisymmetric Automorphisms of the Circle

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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

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics

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