Certain Integrability of Quasisymmetric Automorphisms of the Circle

Katsuhiko Matsuzaki

doi:10.1007/s40315-014-0082-y

Certain Integrability of Quasisymmetric Automorphisms of the Circle

Katsuhiko Matsuzaki^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	487-503
Number of pages	17
Journal	Computational Methods and Function Theory
Volume	14
Issue number	2-3
DOIs	https://doi.org/10.1007/s40315-014-0082-y
Publication status	Published - 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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10.1007/s40315-014-0082-y

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title = "Certain Integrability of Quasisymmetric Automorphisms of the Circle",

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.",

keywords = "Asymptotically conformal, Complex dilatation, Cross-ratio, Liouville cocycle, Quasiconformal map, Quasisymmetric quotient",

author = "Katsuhiko Matsuzaki",

note = "Funding Information: This work was supported by JSPS KAKENHI 24654035. Publisher Copyright: {\textcopyright} 2014, Springer-Verlag Berlin Heidelberg.",

year = "2014",

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doi = "10.1007/s40315-014-0082-y",

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T1 - Certain Integrability of Quasisymmetric Automorphisms of the Circle

AU - Matsuzaki, Katsuhiko

PY - 2014/10/31

Y1 - 2014/10/31

N2 - 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.

AB - 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.

KW - Asymptotically conformal

KW - Complex dilatation

KW - Cross-ratio

KW - Liouville cocycle

KW - Quasiconformal map

KW - Quasisymmetric quotient

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U2 - 10.1007/s40315-014-0082-y

DO - 10.1007/s40315-014-0082-y

M3 - Article

AN - SCOPUS:84919905072

SN - 1617-9447

VL - 14

SP - 487

EP - 503

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

IS - 2-3

ER -

Certain Integrability of Quasisymmetric Automorphisms of the Circle

Abstract

Keywords

ASJC Scopus subject areas

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