Certain Integrability of Quasisymmetric Automorphisms of the Circle

Katsuhiko Matsuzaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number2-3
Publication statusPublished - 2014 Oct 31


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

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Certain Integrability of Quasisymmetric Automorphisms of the Circle'. Together they form a unique fingerprint.

Cite this