Abstract
This article addresses the question of which non-empty, compact, proper subsets E of the extended complex plane C have the feature that, for some K in 1,∞, the family of K-quasiconformal self-mappings of C which leave E invariant acts transitively on the set E×Ec, where Ec is the complement of E in C. The main result in the paper asserts that the class of sets with this property comprises all one- and two-point subsets of C, all quasicircles in C and all images of the Cantor ternary set under quasiconformal self-mappings of C. It is shown that the third category includes the limit set of any non-cyclic, finitely generated Schottky group. 1991 Mathematics Subject Classification: 30C62.
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