TY - JOUR
AU - Palka, Bruce
AB - 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.
TI - Quasiconformally Bi‐Homogeneous Compacta in the Complex Plane
JO - Proceedings of the London Mathematical Society
DO - 10.1112/S0024611599001690
DA - 1999-01-01
UR - https://www.deepdyve.com/lp/wiley/quasiconformally-bi-homogeneous-compacta-in-the-complex-plane-4q9IZB06eF
SP - 215
EP - 240
VL - 78
IS - 1
DP - DeepDyve
ER -