Vol. 28, No. 3, 1969

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On the boundary correspondence of quasiconformal mappings of domains bounded by quasicircles

Terence John Reed

Vol. 28 (1969), No. 3, 653–661
Abstract

A Jordan curve is a quasicircle if there exists a constant C(1 C < ) such that the cross ratio (z1,z2,z3,z4) of any four points z1,,z4 in order on satisfies |(z1,z2,z3,z4)|C. It is shown that the boundary correspondence f induced by a quasiconformal homeomorphism of two Jordan domains bounded by quasicircles satisfies |(w1,w2,w3,w4)|A|(z1,z2,z3,z4)|α, (A 1,0 < α 1) where wk = f(zk) and the points are in order on the boundary. A converse to this result is proved and estimates are computed in each direction.

Mathematical Subject Classification
Primary: 30.47
Milestones
Received: 18 April 1968
Revised: 5 July 1968
Published: 1 March 1969
Authors
Terence John Reed