TY - JOUR
T1 - Non-existence of prescribable conformally equivariant dilatation in space
AU - Chaiya, Malinee
AU - Hinkkanen, Aimo
PY - 2013
Y1 - 2013
N2 - In this paper, we study the prescribable conformally equivariant dilatations for orientation preserving quasiconformal homeomorphisms. The complex dilatation is a prescribable conformally equivariant dilatation in ℝ2. A Schottky set is a subset of the unit sphere Sn whose complement is the union of at least three disjoint open balls. By using the result of Bonk, Kleiner, and Merenkov that there are rigid Schottky sets of positive measure in each dimension at least 3, we prove that it is not possible to have a prescribable conformally equivariant dilatation in ℝn, where n ≥ 3.
AB - In this paper, we study the prescribable conformally equivariant dilatations for orientation preserving quasiconformal homeomorphisms. The complex dilatation is a prescribable conformally equivariant dilatation in ℝ2. A Schottky set is a subset of the unit sphere Sn whose complement is the union of at least three disjoint open balls. By using the result of Bonk, Kleiner, and Merenkov that there are rigid Schottky sets of positive measure in each dimension at least 3, we prove that it is not possible to have a prescribable conformally equivariant dilatation in ℝn, where n ≥ 3.
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U2 - 10.1090/S0002-9939-2013-11692-8
DO - 10.1090/S0002-9939-2013-11692-8
M3 - Article
AN - SCOPUS:84882694071
SN - 0002-9939
VL - 141
SP - 3985
EP - 3995
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 11
ER -