TY - JOUR
T1 - Certain Integrability of Quasisymmetric Automorphisms of the Circle
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
This work was supported by JSPS KAKENHI 24654035.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
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 -