The Structure of Certain Quasisymmetric Groups
Aimo Hinkkanen
jan. 1990 · American Mathematical Soc.
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A quasisymmetric mapping is a homeomorphism of the circle with the property that it does not distort cross ratios too badly. By a theorem of Beurling and Ahlfors such maps are precisely the boundary values of quasiconformal homeomorphisms of the disk. A group [italic]G of quasisymmetric mappings of the circle is called a quasisymmetric group if there is a uniform upper bound on the distortion of each [script lowercase]g in [italic]G. If this upper bound is [italic]K we call [italic]G a [italic]K-quasisymmetric group. In this paper the author continues the study of these groups, in particular the question of when such groups are quasisymmetrically conjugate to conformal groups.
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